Exponent Calculator — Calculate Powers with Steps

An exponent calculator finds the value of a number raised to a power. For example, 2^10 = 1,024. Enter the base and exponent above to calculate the power instantly and view the steps.

An exponent counts repeated multiplication. The expression a^b means the base a is used b times when b is a positive integer. 2^5 = 2 × 2 × 2 × 2 × 2 = 32. The exponent is the 5. The power is the whole expression, or the value 32.

A negative exponent flips the value into a reciprocal. A fractional exponent mixes a root and a power. A logarithm is the inverse question: which exponent produces a given result. That reverse step belongs on the Logarithm Calculator.

1. Use Evaluate a power for a^b. Use Find the exponent or Find the base when one value is missing.
2. Type integers, decimals, fractions such as 2/3, scientific notation, e, or pi.
3. The result card shows the value, an exact fraction when one is available, and the steps.
4. Copy the result, the steps, or a link. The shared link uses a query string, and the page canonical stays the clean URL.

The basic form is a^b. For a positive integer b, multiply a by itself b times.

a^b

When the exponent is the unknown in a^x = b, and the base is positive and not 1, and the result is positive:

x = ln(b) / ln(a)

That formula is real-number arithmetic. It does not apply to a base of 0, a base of 1, or a negative result. When the base is the unknown, the calculator takes the matching root, and it lists both real solutions when an even exponent has a positive result.

• a^m × a^n = a^(m+n). Same base, add the exponents.
• a^m ÷ a^n = a^(m−n). Same base, subtract the exponents.
• (a^m)^n = a^(mn). A power of a power multiplies the exponents. (2^3)^4 = 2^12 = 4,096.
• a^−n = 1 / a^n, when a is not 0.
• a^(1/n) is the nth root of a, when that root is a real number.
• a^0 = 1 for every nonzero a. This calculator leaves 0^0 undefined.

These rules assume a shared base and real numbers. Adding powers is not one of them: a^m + a^n is not a^(m+n).

A negative exponent means “one over the positive power.” It is a reciprocal, not a sign change.

5^−2 = 1 / 5^2 = 1/25 = 0.04

10^−3 = 0.001. Zero raised to a negative power is undefined here because it would divide by zero.

An exact fraction stays a fraction. 27^(2/3) means the cube root of 27, then that result squared: 3^2 = 9. 16^(3/4) = 8. 81^(1/2) = 9, the same value as the square root.

A decimal such as 0.5 is one half, so 81^0.5 = 9. A long decimal is not rewritten as a guessed fraction. Negative bases are real when the reduced denominator is odd, so (−8)^(1/3) = −2. An even root of a negative number, such as (−9)^(1/2), has no real-number result. For a dedicated root, use the Square Root Calculator, which also handles cube roots and nth roots.

The same job shows up under several names: exponent calculator, power calculator, calculate exponents, and calculate powers. A number to a power calculator, or an x raised to a power calculator, is the same evaluate mode: type the base and the exponent.

A negative exponent calculator, a fractional exponent calculator, and a decimal exponent calculator are the same tool with different inputs. 5^−2, 27^(2/3), and 81^0.5 all belong here. Find exponent, find missing exponent, and solve for exponent use the second mode, which divides two logarithms. The third mode finds the base.

• 2^5 is 32, not 2 × 5. An exponent repeats multiplication. It is not ordinary multiplication by the exponent.
• a^m + a^n is not a^(m+n). You may add exponents only when the powers are multiplied and the bases match.
• (a+b)^2 is not a^2 + b^2. The square of a sum also includes 2ab.
• (−2)^2 = 4 because the parentheses include the minus sign. −2^2 is −(2^2) = −4, because the exponent is applied before the leading minus.

• Logarithm Calculator to find the exponent when you already know the base and the result.
• Square Root Calculator for square roots, cube roots, and nth roots.
• Fraction Calculator when the base or the exponent is a fraction you want to simplify first.
• Scientific Calculator for a keypad that mixes powers with other operations.