Exponent rules
Examples: 2¹⁰ = 1,024. 10⁻³ = 1 ÷ 1,000 = 0.001. 8^(2/3) = (∛8)² = 2² = 4. The cube root of 27 is 3, because 3³ = 27. The cube root of −27 is −3, but the square root of −4 isn't a real number.
For whole-number powers too big for ordinary arithmetic, like 2¹⁰⁰ or 3²⁰⁰, the calculator also works out every digit exactly: 2¹⁰⁰ = 1,267,650,600,228,229,401,496,703,205,376.
Common powers and roots
| n | n² | n³ | √n | ∛n |
|---|---|---|---|---|
| 1 | 1 | 1 | 1.0000 | 1.0000 |
| 2 | 4 | 8 | 1.4142 | 1.2599 |
| 3 | 9 | 27 | 1.7321 | 1.4422 |
| 4 | 16 | 64 | 2.0000 | 1.5874 |
| 5 | 25 | 125 | 2.2361 | 1.7100 |
| 6 | 36 | 216 | 2.4495 | 1.8171 |
| 7 | 49 | 343 | 2.6458 | 1.9129 |
| 8 | 64 | 512 | 2.8284 | 2.0000 |
| 9 | 81 | 729 | 3.0000 | 2.0801 |
| 10 | 100 | 1,000 | 3.1623 | 2.1544 |
| 11 | 121 | 1,331 | 3.3166 | 2.2240 |
| 12 | 144 | 1,728 | 3.4641 | 2.2894 |
For a whole expression with powers, use the scientific calculator.
Frequently asked questions
What is a negative exponent?
A negative exponent means take the reciprocal: x⁻ⁿ = 1 ÷ xⁿ. So 2⁻³ = 1/8 = 0.125.
Why is anything to the power of 0 equal to 1?
Because xⁿ ÷ xⁿ = x^(n−n) = x⁰, and any nonzero number divided by itself is 1. Zero to the power zero is usually defined as 1 in algebra, but it's left undefined in some contexts.
How do I calculate a fractional exponent?
Split it into a root and a power: x^(a/b) means take the b-th root of x, then raise it to the a-th power. For example, 16^(3/4) = (⁴√16)³ = 2³ = 8.
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