Calculate powers of any base and exponent, including negative and fractional values.
Last updated: March 2026 | By ForgeCalc Engineering
An exponent refers to the number of times a number (the base) is multiplied by itself. For example, $2^3$ means $2 * 2 * 2$, which equals 8.
Exponents are a shorthand way of writing repeated multiplication. They are used extensively in science, finance (compound interest), and computer science (binary systems).
Any non-zero number to the power of 0 is 1.
A negative exponent indicates a reciprocal.
Fractional exponents represent roots.
Calculate 5 to the power of -2:
1. Identify base = 5, exponent = -2
2. Use negative rule: 5⁻² = 1 / 5²
3. Calculate 5²: 5 * 5 = 25
4. Result: 1 / 25 = 0.04
Final Answer: 0.04
In most contexts, 0⁰ is considered indeterminate, though in some fields like combinatorics, it is defined as 1.
Use an exponent of 0.5 (1/2). For example, 9 to the power of 0.5 is 3.
If the exponent is even, the result is positive. If odd, the result is negative. For example, (-2)² = 4, but (-2)³ = -8.
It's a way to write very large or small numbers using powers of 10. For example, 1,000,000 is 1 * 10⁶.
A negative exponent indicates a reciprocal. For example, 2^(-3) = 1/(2^3) = 1/8 = 0.125. The base is flipped to the denominator.
A fractional exponent like 2^(3/2) means: take the denominator as a root, then the numerator as a power. So 2^(3/2) = (2^(1/2))^3 = (√2)^3 ≈ 2.83.
They are inverses. If a^b = c, then log_a(c) = b. Logarithms 'undo' exponentiation, and vice versa.
This comes from the exponent rule: a^(m-n) = a^m / a^n. When m = n, we get a^0 = a^m / a^m = 1 (for any non-zero a).
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