Exponent Calculator
Calculate BaseExponent
About Exponent Calculator
Understanding Exponents
An exponent tells you how many times to multiply a base number by itself. In the expression 2^5, the base is 2 and the exponent is 5, meaning 2 x 2 x 2 x 2 x 2 = 32. Exponents are fundamental to science (exponential growth and decay), computing (binary numbers, data storage), finance (compound interest), and virtually all branches of mathematics. They compress very large and very small numbers into manageable notation and appear in formulas ranging from Einstein's E=mc^2 to the compound interest formula.
Exponent Rules
Key exponent laws: a^m x a^n = a^(m+n), a^m / a^n = a^(m-n), (a^m)^n = a^(mn), a^0 = 1 (for any non-zero a), a^(-n) = 1/a^n, and a^(1/n) = nth root of a. These rules allow simplification of complex expressions and are used constantly in algebra and calculus.
How to Use This Calculator
Enter the base number and the exponent (power). The calculator accepts positive and negative bases, integer and decimal exponents, and displays the result in both standard and scientific notation for very large or small results. Fractional exponents are supported, allowing you to calculate roots and powers simultaneously.
Frequently Asked Questions
What is a negative exponent?
A negative exponent means take the reciprocal. 2^(-3) = 1/(2^3) = 1/8. It does not make the result negative.
What is anything raised to the power of zero?
Any non-zero number raised to the power of zero equals 1. This is true by convention and consistent with exponent rules: a^n / a^n = a^(n-n) = a^0 = 1.
What is a fractional exponent?
A fractional exponent combines a root and a power. a^(m/n) means take the nth root of a, then raise it to the mth power. For example, 8^(2/3) = (cube root of 8)^2 = 2^2 = 4.
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