Exponent Calculator - Powers & Exponent Laws

How Exponents Work

Exponents are shorthand for repeated multiplication, and they power everything from compound interest to computer memory sizes. The key idea: the exponent counts multiplications, so 10^3 means three tens multiplied together.

Solving Exponential Equations

When the unknown is in the exponent — like 3^x = 81 — logarithms undo the exponent. Take the log of both sides and the exponent drops down: x = log(81) ÷ log(3) = 4. This is exactly how the solve mode works.

Negative and Fractional Exponents

A negative exponent means “reciprocal”: 2^(−3) = 1/8. A fractional exponent means “root”: 16^(1/2) = √16 = 4. Both follow from the same laws, just run in reverse.

Working with roots and powers together? Try our scientific calculator or learn about the inverse operation with the logarithm calculator.

Frequently Asked Questions

What is an exponent?

An exponent tells you how many times to multiply the base by itself. In 2^5, the base is 2 and the exponent is 5, so 2^5 = 2 × 2 × 2 × 2 × 2 = 32.

How do you solve an equation like 2^x = 32?

Take the logarithm of both sides: x = log(32) ÷ log(2) = 5. The solve mode above does this automatically and shows each step.

What are the main laws of exponents?

Same base: add exponents when multiplying (a^m × a^n = a^(m+n)), subtract when dividing. Power of a power multiplies exponents: (a^m)^n = a^(mn). See the laws tab for the full list.

Is this calculator free?

Yes — every tool on Math Solver Free is free with no sign-up, and all calculations run in your browser.