The exponent that a number states how countless times to use the number in a multiplication.
You are watching: 10 to the power of -3
In 82 the "2" claims to usage 8 double in a multiplication,so 82 = 8 × 8 = 64
In words: 82 might be dubbed "8 come the power 2" or "8 to the second power", or merely "8 squared"
Exponents are additionally called powers or Indices.
Some an ext examples:
Example: 53 = 5 × 5 × 5 = 125
In words: 53 might be dubbed "5 come the 3rd power", "5 come the strength 3" or merely "5 cubed"Example: 24 = 2 × 2 × 2 × 2 = 16
In words: 24 might be referred to as "2 to the fourth power" or "2 to the power 4" or merely "2 come the 4th"So in general:
| an tells you to multiply a by itself,so there are n the those a"s: |  |
Another way of composing It
Sometimes human being use the ^ prize (above the 6 on her keyboard), together it is simple to type.
Negative Exponents
Negative? What might be the contrary of multiplying? Dividing!
So we divide by the number each time, i m sorry is the very same as multiply by 1number
Negative? flip the Positive!
 | That last example showed one easier method to handle an adverse exponents: calculate the confident exponent (an) |
More Examples:
| 4-2 | = | 1 / 42 | = | 1/16 = 0.0625 |
| 10-3 | = | 1 / 103 | = | 1/1,000 = 0.001 |
| (-2)-3 | = | 1 / (-2)3 | = | 1/(-8) = -0.125 |
What if the Exponent is 1, or 0?
| 1 | If the exponent is 1, climate you just have actually the number chin (example 91 = 9) | |
| 0 | If the exponent is 0, then you gain 1 (example 90 = 1) | |
| But what about 00 ? It might be one of two people 1 or 0, and so civilization say it is "indeterminate". |
It All provides Sense
If girlfriend look at the table, girlfriend will view that positive, zero ornegative exponents space really component of the exact same (fairly simple) pattern:
| .. Etc.. See more: We Were Young When I Was Young I Fell In Love With You First |  | ||
| 52 | 5 × 5 | 25 | |
| 51 | 5 | 5 | |
| 50 | 1 | 1 | |
| 5-1 | 15 | 0.2 | |
| 5-2 | 15 × 15 | 0.04 | |
| .. Etc.. |