Exponent Calculator

Simplify powers and solve exponential equations with the exponent laws shown clearly.

Drag & drop or upload an image or PDF

Enter a power or equation, such as (x^3 x^5)/x^2

Try an example

Exponents describe repeated multiplication

Exponent rules make large products compact, but the rules depend on matching bases and on whether powers are multiplied, divided, or raised again.

Negative exponents create reciprocals, not negative values. Rational exponents connect powers with roots. For exponential equations, rewriting both sides with a common base is often the cleanest first move.

How to use the exponent calculator

Enter the problem as written

Type or paste the full expression. You can also upload a clear photo or PDF and check the extracted text before solving.

Read the working, not only the answer

Each transformation is separated and explained so you can compare it with your own method.

Ask about any step

Continue in the same solution to request another method, check a restriction, or ask why a rule applies.

Core exponent laws

These laws apply to matching nonzero bases. The operation outside the powers determines what happens to the exponents.

a^{m} a^{n} = a^{m + n}, \frac{a ^{m}}{a ^{n}} = a^{m - n}, (a^{m})^{n} = a^{mn}

A reliable way to work through it

Match the bases

Rewrite numerical powers with a common base when possible.

Apply one exponent law at a time

Keep product, quotient, and power-of-a-power rules separate to avoid mixing them.

Rewrite negative powers

Move a factor across the fraction bar and make its exponent positive.

Worked example

Simplify (x³ · x⁵) / x²

x^{3 + 5}

Add exponents when multiplying equal bases.

\frac{x ^{8}}{x ^{2}} = x^{8 - 2}

Subtract exponents when dividing equal bases.

x^{6}

Simplify the exponent.

For x not equal to zero, the expression simplifies to x⁶.

Common mistakes to check

Adding exponents across addition

The product rule applies to multiplication, not to aᵐ + aⁿ.

Treating a negative exponent as a negative number

a⁻ⁿ means 1/aⁿ when a is not zero.

Forgetting to power every factor

In (ab)ⁿ, the exponent applies to both a and b.

Logarithm CalculatorEvaluate, expand, condense, or solve logarithms while keeping every domain restriction visible.Simplify CalculatorCombine like terms, reduce fractions, and rewrite expressions in a cleaner equivalent form.Polynomial CalculatorWork with polynomial operations, factors, roots, and remainders in one place.Solve for X CalculatorEnter an equation and see how to isolate x, simplify both sides, and check the result.

Questions students ask

Can the calculator simplify negative exponents?

Yes. It rewrites them as reciprocals and explains any restrictions caused by zero denominators.

Can it work with fractional exponents?

Yes. Rational exponents can be rewritten as roots, such as x^(1/2) = √x.

Does it solve exponential equations?

Yes. It can match bases or use logarithms when a common-base rewrite is not available.

What is any nonzero number to the zero power?

It equals 1. The expression 0⁰ is a separate indeterminate case in many contexts.