Raise a number to any power, including negative and fractional exponents, and see the reciprocal and square root of the result.
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Enter your numbers to see a result.
With base (b) 2, exponent (n) 10, the result is 1,024.
| Base (b) | 2 |
|---|---|
| Exponent (n) | 10 |
| Result | 1,024 |
|---|---|
| Reciprocal (1 ÷ result) | 0.0009765625 |
| Square root of the result | 32 |
Enter the base and the exponent. Whole-number exponents mean repeated multiplication, negative exponents mean the reciprocal, and fractional exponents mean roots: 8^(1/3) is the cube root of 8, which is 2. A negative base needs a whole-number exponent, because a fractional power of a negative number is not a real number.
bⁿ = b × b × … × b (n times). b⁻ⁿ = 1 ÷ bⁿ. b^(p/q) = (q-th root of b)^p. b⁰ = 1. Enter the base and the exponent. Whole-number exponents mean repeated multiplication, negative exponents mean the reciprocal, and fractional exponents mean roots: 8^(1/3) is the cube root of 8, which is 2. A negative base needs a whole-number exponent, because a fractional power of a negative number is not a real number.
With base (b) 2, exponent (n) 10, the result is 1,024. Reciprocal (1 ÷ result): 0.0009765625; Square root of the result: 32.
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It means the reciprocal of the positive power. 2⁻³ = 1 ÷ 2³ = 1 ÷ 8 = 0.125.
The denominator is a root and the numerator a power. 27^(2/3) is the cube root of 27 (which is 3), squared, giving 9.
Each step down in the exponent divides by the base: 2³ = 8, 2² = 4, 2¹ = 2, so 2⁰ = 1. The pattern holds for every non-zero base.