An exponent tells you how many times to multiply a number (the base) by itself. For example, 2^3 = 2 × 2 × 2 = 8. The base is 2 and the exponent is 3.

What happens when you raise a number to the power of 0?

Any non-zero number raised to the power of 0 equals 1. For example, 5^0 = 1, 100^0 = 1. This is a mathematical convention that maintains consistency with the laws of exponents.

What does a negative exponent mean?

A negative exponent means you take the reciprocal. For example, 2^(-3) = 1/(2^3) = 1/8 = 0.125. So x^(-n) = 1/(x^n).

Free Exponent Calculator — Powers and Roots

Understanding Exponents and Powers

Exponents are a shorthand way of expressing repeated multiplication. When you write 2¹⁰, it means multiplying 2 by itself 10 times: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024. The base (2) is the number being multiplied, and the exponent (10) tells you how many times to multiply it.

Several special cases are worth knowing. Any number raised to the power of 1 equals itself (x¹ = x). Any non-zero number raised to the power of 0 equals 1 (x⁰ = 1). Negative exponents produce reciprocals: x^-n = 1/xⁿ. Fractional exponents represent roots: x^1/n = ⁿ√x. This calculator supports all of these cases.

For very large or very small results, the calculator automatically displays scientific notation alongside the standard result. Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10. For example, 2⁵⁰ = 1,125,899,906,842,624 is displayed as 1.126 × 10¹⁵. The nth root mode computes x^1/n, which is the inverse operation of exponentiation. Exponents are fundamental to compound interest calculations, computer science (binary systems), physics, and engineering.

Exponent Calculator

Understanding Exponents and Powers

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