{"id":37747,"date":"2026-01-22T12:45:45","date_gmt":"2026-01-22T12:45:45","guid":{"rendered":"https:\/\/mp.moonpreneur.com\/math-corner\/?p=37747"},"modified":"2026-03-30T13:24:05","modified_gmt":"2026-03-30T13:24:05","slug":"exponential-equations-using-recursion-and-algebraic","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/exponential-equations-using-recursion-and-algebraic\/","title":{"rendered":"Solving Exponential Equations Using Recursion and Algebraic Method"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"37747\" class=\"elementor elementor-37747\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-fcfec80 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fcfec80\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-92390b3\" data-id=\"92390b3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0fa4990 elementor-widget elementor-widget-text-editor\" data-id=\"0fa4990\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">We\u2019ve all been there: You\u2019re staring at an SAT practice test, and suddenly you see a problem like <i>x<\/i>+ 1\/x = 1. <b>Find the value of \\(\\displaystyle x^{2021} + \\frac{1}{x^{2021}}\\)\u00a0<br \/><\/b><\/span><\/p><p><span style=\"font-weight: 400;\">At first glance, you might think. How are you supposed to calculate something to the power of 2021 without a supercomputer? But today, in this blog, we are going to solve this without a supercomputer, using two brilliant approaches.<\/span><\/p><h4><span style=\"color: #008000;\"><b>Method 1: The Power of Patterns (The Recursive Approach)<\/b><\/span><\/h4><p><span style=\"font-weight: 400;\">When you see a massive exponent, there is almost always a hidden pattern. Instead of jumping to 2021, let&#8217;s start small and see what happens when we increase the power of x step by step.<\/span><\/p><ol><li><span style=\"font-weight: 400;\"><strong> Starting Point<\/strong>: We know x+ 1\/x =1. Let&#8217;s call this f(1).<\/span><\/li><li><b class=\"ng-star-inserted\" data-start-index=\"1002\">Squaring it:<\/b><span class=\"ng-star-inserted\" data-start-index=\"1014\"> If we square both sides, we get x\u00b2 + 1\/x + 2 = 1\u00b2. Subtracting<\/span><span class=\"ng-star-inserted\" data-start-index=\"1068\">\u00a02 gives us x\u00b2 + 1\/x\u00b2<\/span><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">\u00a0<\/span><\/span><span class=\"mrel\">= <\/span><\/span><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"ng-star-inserted\" data-start-index=\"1109\">. Let&#8217;s call this <\/span><span class=\"ng-star-inserted\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">).<\/span><\/span><\/span><\/span><\/span><\/li><li><b class=\"ng-star-inserted\" data-start-index=\"1132\">Cubing it:<\/b><span class=\"ng-star-inserted\" data-start-index=\"1142\"> By multiplying these two results together, we can find <\/span><span class=\"ng-star-inserted\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">x\u00b3 <\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">1\/<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x\u00b3<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"ng-star-inserted\" data-start-index=\"1209\">.\u00a0 After some quick algebra, we find that x\u00b3 + 1\/x\u00b3 = \u22122.<\/span><\/li><\/ol><p><span style=\"font-weight: 400;\"><strong>Recommended Reading<\/strong>: <a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/american-mathematics-competitions\/\">American Mathematics Competitions (AMC) Guide<\/a><\/span><\/p><p><b>The Decisive Moment<\/b><span style=\"font-weight: 400;\">: If you keep going, you\u2019ll discover a recursive formula: each step can be found using the ones before it. The relationship is <\/span><span style=\"font-weight: 400;\">f(n) = f(n\u22121) \u2212f (n\u22122)<\/span><span style=\"font-weight: 400;\">. Using this, we can list the values:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><i><span style=\"font-weight: 400;\">\u00a0f<\/span><\/i><span style=\"font-weight: 400;\">(1)=1<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00a0<\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">(2)=\u22121<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00a0<\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">(3)=\u22122<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00a0<\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">(4)=\u22121<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00a0<\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">(5)=1<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00a0<\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">(6)=2<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">f(7)=1 &#8230; wait, it&#8217;s repeating.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">The values repeat <\/span><b>every six steps<\/b><span style=\"font-weight: 400;\">. To find the value for 2021, we just divide 2021 by 6. The remainder is <\/span><b>5<\/b><span style=\"font-weight: 400;\">, which means the value of \\(\\displaystyle x^{2021} + \\frac{1}{x^{2021}}\\) is the same as <i>f<\/i>(5), which is\u00a0<b>1.<\/b><\/span><\/p><h4><span style=\"color: #008000;\"><b>Method 2: The \u201cAlgebraic method (The <\/b><b><i>x<\/i><\/b><b><i>\u00b3 <\/i><\/b><b>Shortcut)<\/b><\/span><\/h4><p><span style=\"font-weight: 400;\">If recursion feels too long, there is a faster algebraic way that often appears on advanced math competitions and the SAT.<\/span><\/p><p><span style=\"font-weight: 400;\">If you take the original equation <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">+1\/<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">=1<\/span><span style=\"font-weight: 400;\"> and rearrange it into a quadratic equation, you get\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x\u00b2 &#8211; x + 1 = 0.<\/span><\/p><h5><span style=\"color: #800080;\"><b>Now, here is the trick<\/b><span style=\"font-weight: 400;\">:\u00a0<\/span><\/span><\/h5><p><span style=\"font-weight: 400;\">If you multiply that equation by <\/span><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">+1)<\/span><span style=\"font-weight: 400;\">, you get a very famous identity: <\/span><i><span style=\"font-weight: 400;\">x\u00b3<\/span><\/i><span style=\"font-weight: 400;\"> + 1 = 0<\/span><span style=\"font-weight: 400;\">.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">This tells us that for this problem, <\/span><i><span style=\"font-weight: 400;\">x\u00b3<\/span><\/i><span style=\"font-weight: 400;\"> = \u22121 , We can rewrite \\(\\displaystyle x^{2021}\\) using x\u00b3.<br \/><\/span><\/p><ul><li><i><\/i><i><span style=\"font-weight: 400;\">2021 = (3\u00d7673) + 2<\/span><\/i><\/li><li>So, \\(\\displaystyle x^{2021} = (x^{3})^{673} \\times x^{2}\\)<\/li><li>Since, x\u00b3 = -1 <i><span style=\"font-weight: 400;\">this becomes \\(\\displaystyle (-1)^{673} \\times x^{2} = -x^{2}\\)\u00a0<br \/><\/span><\/i><\/li><\/ul><p>Doing the same for \\(\\displaystyle \\frac{1}{x^{2021}} \\)\u00a0 gives us -1\/x\u00b2.\u00a0 <span class=\"ng-star-inserted\" data-start-index=\"2516\">The whole problem simplifies to <\/span><span class=\"ng-star-inserted\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x\u00b2 <\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">1\/<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x\u00b2<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><span class=\"ng-star-inserted\" data-start-index=\"2562\">.<\/span><\/p><p><span class=\"ng-star-inserted\" data-start-index=\"2562\"> Since we already found that x\u00b2 +<\/span><span class=\"ng-star-inserted\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mbin\">\u00a0<\/span><\/span><span class=\"base\"><span class=\"mord\">1\/<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x\u00b2 <\/span><\/span><span class=\"mrel\">= <\/span><\/span><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><span class=\"ng-star-inserted\" data-start-index=\"2608\">, the final answer is \u2212(\u22121) = 1.<\/span><\/p><h5><span style=\"color: #800080;\"><strong>For a more detailed walkthrough, you can watch this video: <\/strong><\/span><\/h5>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f1092aa elementor-widget elementor-widget-video\" data-id=\"f1092aa\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/A194EmMWVJY?si=y6gBpToXEykS2mhK&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-000fa3b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"000fa3b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1901152\" data-id=\"1901152\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-efb1fbf elementor-widget elementor-widget-text-editor\" data-id=\"efb1fbf\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h4><span style=\"color: #0000ff;\"><b>The Takeaway for Your SAT Journey<\/b><\/span><\/h4><p><span style=\"font-weight: 400;\">Whether you prefer finding a repeating cycle or using algebraic identities, the lesson is the same: Don&#8217;t be intimidated by big numbers.<\/span><\/p><p><span style=\"font-weight: 400;\">The SAT tests your ability to spot these structures. Next time you see a giant exponent, don&#8217;t reach for a calculator\u2014reach for a pattern.<\/span><\/p><p><b>Recommended Reading:<\/b><\/p><ol><li><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/derive-quadratic-formula\/\"><span style=\"font-weight: 400;\">How to Derive and Use the Quadratic Formula (With Examples)<\/span><\/a><\/li><li><p><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/sherman-morrison-woodbury-identity\/\"><span style=\"font-weight: 400;\">Application &amp; Proof\u00a0 of the Sherman-Morrison-Woodbury Identity<\/span><\/a><\/p><\/li><li><p><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/sat-quadratics-tricks\/\">The Ultimate Guide to Solving SAT Quadratics in Seconds<\/a><\/p><\/li><li><p><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/geometry-problem\/\"><span>Interesting Geometry Problem to Solve For Kids<\/span><\/a><\/p><\/li><li><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/linear-equations-different-solutions\/\"><span style=\"font-weight: 400;\">Linear Equation &#8211; One Solution, No Solution and Many Solutions<\/span><\/a><\/li><\/ol><p><span style=\"font-weight: 400;\">Want to excite your child about math and sharpen their math skills? Moonpreneur&#8217;s online math curriculum is unique as it helps children understand math skills through hands-on lessons, assists them in building real-life applications, and excites them to learn math.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">You can opt for our <\/span><a href=\"https:\/\/moonpreneur.com\/innovator-program\/advanced-math\/\"><span style=\"font-weight: 400;\">Advanced Math<\/span><\/a><span style=\"font-weight: 400;\"> or Vedic Math+Mental Math courses. Our <\/span><a href=\"https:\/\/mp.moonpreneur.com\/math-quiz-for-kids\/\"><span style=\"font-weight: 400;\">Math Quiz<\/span><\/a><span style=\"font-weight: 400;\"> for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.<\/span><\/p><p><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/wp-content\/uploads\/2026\/01\/Solving-Exponential-Equations-Using-Recursion-And-Algebraic-Method.jpeg\"><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-37757\" src=\"https:\/\/mp.moonpreneur.com\/math-corner\/wp-content\/uploads\/2026\/01\/Solving-Exponential-Equations-Using-Recursion-And-Algebraic-Method.jpeg\" alt=\"Solving-Exponential Equations-Using Recursion-And- Algebraic-Method\" width=\"1600\" height=\"893\" \/><\/a><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-4dd7e1e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4dd7e1e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-70c82a2\" data-id=\"70c82a2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-eb6ea7a elementor-widget elementor-widget-text-editor\" data-id=\"eb6ea7a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><strong>FAQs on Exponential Equations<\/strong><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-44c18e9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"44c18e9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-24f8067\" data-id=\"24f8067\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b4d1436 elementor-widget elementor-widget-elementskit-faq\" data-id=\"b4d1436\" data-element_type=\"widget\" data-widget_type=\"elementskit-faq.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div class=\"ekit-wid-con\">\n                <div class=\"elementskit-single-faq elementor-repeater-item-95228b5\">\n            <div class=\"elementskit-faq-header\">\n                <h2 class=\"elementskit-faq-title\">1. How can I solve for a massive exponent like 2021 without a calculator? <\/h2>\n            <\/div>\n            <div class=\"elementskit-faq-body\">\n                Ans. The secret is to look for a repeating pattern or cycle. By calculating the first few values of the expression, you can discover a recursive formula, which in this case is f(n)=f(n\u22121)\u2212f(n\u22122). In this specific problem, the values repeat every six steps. Once you identify the cycle, you simply divide the large exponent (2021) by the cycle length (6) to find the remainder, which tells you exactly where in the sequence the answer lies.            <\/div>\n        <\/div>\n                <div class=\"elementskit-single-faq elementor-repeater-item-d0e977e\">\n            <div class=\"elementskit-faq-header\">\n                <h2 class=\"elementskit-faq-title\">2. Why do both the recursive and algebraic methods give the same answer? <\/h2>\n            <\/div>\n            <div class=\"elementskit-faq-body\">\n                Ans. Both methods are different paths to the same mathematical truth. The recursive method identifies that the 5th step in the cycle is 1. Similarly, the algebraic method simplifies the entire problem down to \u2212(x\u00b2 + 1\/x\u00b2). Since the initial steps of the problem show that x\u00b2+1\/x\u00b2=\u22121, the final algebraic result is \u2212(\u22121), which also equals.            <\/div>\n        <\/div>\n                <div class=\"elementskit-single-faq elementor-repeater-item-62a8206\">\n            <div class=\"elementskit-faq-header\">\n                <h2 class=\"elementskit-faq-title\">3. Can this problem be solved using more advanced maths like trigonometry? <\/h2>\n            <\/div>\n            <div class=\"elementskit-faq-body\">\n                Ans. Yes, there is a third method involving Euler\u2019s formula, where you express x in the form ei\u03b8. By expanding this into cos \u03b8 and sin \u03b8 terms, calculating large powers becomes much simpler, although this technique is usually considered more advanced than standard algebra.            <\/div>\n        <\/div>\n        \n    <\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>We\u2019ve all been there: You\u2019re staring at an SAT practice test, and suddenly you see a problem like x+ 1\/x = 1. Find the value of \u00a0 At first glance, you might think. How are you supposed to calculate something to the power of 2021 without a supercomputer? But today, in this blog, we are [&hellip;]<\/p>\n","protected":false},"author":116,"featured_media":38037,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[979,1034],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/37747"}],"collection":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/comments?post=37747"}],"version-history":[{"count":16,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/37747\/revisions"}],"predecessor-version":[{"id":38276,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/37747\/revisions\/38276"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media\/38037"}],"wp:attachment":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media?parent=37747"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/categories?post=37747"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/tags?post=37747"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}