Exponent Calculator — raise a base to a power

How it works

An exponent (or power) is shorthand for repeated multiplication. In base^n, the base is the number being multiplied and the exponent n is how many times:

base^n = base × base × … × base (n times)

So 3^4 = 3 × 3 × 3 × 3 = 81. Two rules extend this beyond whole-number exponents:

• A negative exponent flips to a reciprocal: base^(−n) = 1 ÷ base^n. So 2^(−3) = 1 ÷ 8 = 0.125.
• A fractional exponent is a root: base^(1/n) is the nth root, so 8^(1/3) = 2.

And anything to the power 0 is 1 — the empty product.

Worked example

Compute 2^10:

2^10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

Powers of 10 are especially handy: 10^3 = 1000, since each power adds a zero. A negative exponent gives a small number: 5^(−2) = 1 ÷ 5² = 1 ÷ 25 = 0.04.

Frequently asked questions

How do I calculate an exponent?

Multiply the base by itself as many times as the exponent says. For 4^3, that's 4 × 4 × 4 = 64. For large exponents this grows fast, which is exactly why the notation exists — writing 2^20 is easier than a chain of twenty 2s.

What does a negative exponent mean?

It means take the reciprocal: base^(−n) = 1 ÷ base^n. So 10^(−2) = 1 ÷ 100 = 0.01, and 2^(−1) = 1 ÷ 2 = 0.5. The minus sign flips the power into a division rather than making the result negative.

What does a fractional exponent mean?

It's a root. base^(1/n) is the nth root of the base, so 16^(1/2) = √16 = 4 and 27^(1/3) = ∛27 = 3. A more general fraction combines both: 8^(2/3) = (8^(1/3))² = 2² = 4. Powers and roots are the same operation seen from two sides.

Why is any number to the power of 0 equal to 1?

Because of the pattern of dividing by the base each time the exponent drops by one: 2^3 = 8, 2^2 = 4, 2^1 = 2, and 2^0 = 1. It also keeps the exponent rules consistent (base^n ÷ base^n = base^0 = 1). The one debated case, 0^0, is commonly taken as 1 by convention.

What's the difference between the base and the exponent?

The **base** is the number being multiplied; the **exponent** is how many times. They aren't interchangeable — 2^3 = 8 but 3^2 = 9. Swapping them usually changes the answer, so keep the base on the bottom and the power up top.

How are exponents and logarithms related?

They're inverses. If base^n = x, then log to that base of x is n — the logarithm answers "what exponent produces this number?". So 10^3 = 1000 and log₁₀(1000) = 3 say the same thing two ways.