Power & Root Calculator Guide: Exponents and Roots Explained
Powers and roots are inverse operations — fundamental to compound interest, physics, and engineering. Understanding them unlocks most of advanced mathematics.
Powers Reference Table
| Base | ² (Square) | ³ (Cube) | ⁴ | ⁵ |
|---|---|---|---|---|
| 2 | 4 | 8 | 16 | 32 |
| 3 | 9 | 27 | 81 | 243 |
| 4 | 16 | 64 | 256 | 1,024 |
| 5 | 25 | 125 | 625 | 3,125 |
| 10 | 100 | 1,000 | 10,000 | 100,000 |
Exponent Laws
Frequently Asked Questions
What is a power (exponent)?
A power means multiplying a number by itself a specified number of times. bⁿ = b × b × b... (n times). For example, 2⁵ = 2×2×2×2×2 = 32. The base is 2, the exponent is 5.
What is a square root?
The square root of a number n is the value that, when multiplied by itself, gives n. √n = x means x² = n. For example, √144 = 12 because 12² = 144. Every positive number has two square roots: one positive and one negative.
What is an nth root?
The nth root of a number is the value that, when raised to the power n, gives the original number. The cube root ∛8 = 2 because 2³ = 8. The 4th root ∜81 = 3 because 3⁴ = 81.
What is a negative exponent?
A negative exponent means reciprocal. b⁻ⁿ = 1 ÷ bⁿ. For example, 2⁻³ = 1 ÷ 2³ = 1/8 = 0.125. Any non-zero number raised to the power 0 equals 1: b⁰ = 1.
What is a fractional exponent?
A fractional exponent represents a root. b^(1/n) = n√b. For example, 8^(1/3) = ∛8 = 2. And b^(m/n) = (n√b)^m. So 8^(2/3) = (∛8)² = 2² = 4.
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