| Expression | Answer |
|---|---|
| 105 | 100,000 (one hundred thousand) |
When evaluating what is 10 to the power of 5, it means multiplying the base number 10 by itself 5 times (10×10×10×10×10). A simple shortcut for powers of 10 is to write the number 1 followed by the total number of zeros indicated by the exponent—in this case, 5 zeros.
Recommended reading: What is 2 to the Power of 6?
Quick Summary & Core Values
| Expression | Mathematical Notation | Expanded Form | Final Value |
|---|---|---|---|
| 10 to the power of 5 | 105 | 10 × 10 × 10 × 10 × 10 | 100,000 |
| 10 to the power of -5 | 10-5 | 1 ÷ 105 = 1 ÷ 100,000 | 0.00001 |
How to Calculate 10 to the Power of 5
Understanding exponential notation relies on two basic elements: the base and the exponent.
- Base: The number being multiplied (10).
- Exponent: How many times to multiply the base by itself (5).
Step-by-Step Breakdown:
- 10×10=100 (102)
- 100×10=1,000 (103)
- 1,000×10=10,000 (104)
- 10,000×10=100,000 (105)
What is 10 to the Power of -5?
A negative exponent indicates the reciprocal of the positive power. To solve 10 to the power of -5, flip the base to the denominator:
10−5=1051=100,0001=0.00001
- Decimal Shortcut: For negative powers of 10, move the decimal point 5 places to the left starting from 1.0, which results in 0.00001 (one hundred-thousandth).
Recommended reading: The Wallis Formula: Integrating Powers of Sine and Cosine Instantly
Common Powers of 10 Reference Table
| Power | Power of 10 | Scientific Notation | Standard Form | Word Form |
|---|---|---|---|---|
| 106 | 1 × 106 | 1,000,000 | One Million | |
| 105 | 1 × 105 | 100,000 | One Hundred Thousand | |
| 104 | 1 × 104 | 10,000 | Ten Thousand | |
| 103 | 1 × 103 | 1,000 | One Thousand | |
| 10-1 | 1 × 10-1 | 0.1 | One Tenth | |
| 10-5 | 1 × 10-5 | 0.00001 | One Hundred-Thousandth |
Conclusion
Frequently Asked Questions
How many zeros are in 10 to the power of 5?
There are exactly 5 zeros in 105. Since 105 = 100,000, the number has five zeros.
Why is 10 to the power of 5 written as 105?
The superscript 5 is called an exponent. It means that 10 is multiplied by itself five times: 10 × 10 × 10 × 10 × 10 = 100,000.
Is 105 the same as 10 times 5?
No. 10 × 5 = 50, while 105 = 100,000. An exponent indicates repeated multiplication, not ordinary multiplication.
