Exponent and Power Calculator

Calculate powers, exponents, and exponential expressions with support for any base and exponent.

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1. Enter the base number in the base input field. 2. Enter the exponent (power) in the exponent field - supports positive, negative, and decimal exponents. 3. View the calculated result displayed instantly with full precision. 4. Review the exponent rule explanation showing how the calculation works. 5. Click the copy button to copy the result.

About This Tool

The Exponent and Power Calculator computes the result of raising any base to any exponent. Enter a base number and an exponent (including negative, fractional, and decimal exponents), and get the result instantly. The tool handles integer powers, fractional powers (which are roots), negative exponents, and zero as an exponent.

Exponentiation is one of the most fundamental operations in mathematics, appearing everywhere from compound interest calculations and population growth models to physics equations and computer science algorithms. Understanding how powers work - and being able to compute them quickly - is essential for students and professionals alike.

The calculator provides exact results when possible and high-precision decimal approximations for irrational results. It also explains the rules being applied, such as why a negative exponent gives a reciprocal or why a fractional exponent represents a root. This makes it both a computational tool and an educational resource for learning exponent rules.

Formula / How It Works

a^n = a x a x ... x a (n times) | a^(-n) = 1/a^n | a^(m/n) = n-th root of a^m

Frequently Asked Questions

A negative exponent means the reciprocal of the base raised to the positive exponent. For example, 2^-3 = 1 / 2^3 = 1/8 = 0.125. Any non-zero number raised to a negative power gives a fraction.
Any non-zero number raised to the power of 0 equals 1. For example, 5^0 = 1, 100^0 = 1, and (-3)^0 = 1. The expression 0^0 is a special case that is typically defined as 1 in most contexts.
A fractional exponent represents a root. The denominator is the root and the numerator is the power. For example, 8^(2/3) means the cube root of 8 squared: cube root of 8 is 2, and 2 squared is 4. So 8^(2/3) = 4.
When multiplying powers with the same base, add the exponents: a^m x a^n = a^(m+n). For example, 2^3 x 2^4 = 2^7 = 128.

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