Exponent Calculator
Calculate powers, roots, squares, and cubes. From simple squaring to nth roots, this is your complete exponent toolkit — the E in GEMS.
Powers and Exponents Explained
An exponent tells you how many times to multiply a number (the base) by itself. For example, 2⁴ = 2 × 2 × 2 × 2 = 16.
Common Powers Reference
| Expression | Result | Read As |
|---|---|---|
2¹⁰ |
1,024 | Two to the tenth |
2²⁰ |
1,048,576 | Two to the twentieth (≈ 1 million) |
10³ |
1,000 | Ten cubed (one thousand) |
10⁶ |
1,000,000 | Ten to the sixth (one million) |
√2 |
1.41421… | Square root of two |
e¹ |
2.71828… | Euler’s number |
Special Exponent Rules
- x⁰ = 1 — any number to the power of zero equals one
- x¹ = x — any number to the power of one is itself
- x⁻ⁿ = 1/xⁿ — negative exponents mean reciprocals
- x^(1/n) = ⁿ√x — fractional exponents are roots
- (xᵃ)(xᵇ) = x^(a+b) — multiply powers by adding exponents
The E in GEMS
The E in GEMS stands for Exponent — a nod to the exponential growth that underlies compound interest, population dynamics, computer science, and the universe itself. Every calculation starts with gems. ✦