Raise any number to any power.
Enter a base and an exponent to see the result instantly, plus the square, cube, square root and reciprocal, and the full table of powers. Negative and decimal exponents welcome.
Your numbers
Use a negative exponent for a reciprocal (2-3 = 1/8) or a fraction like 0.5 for a root (90.5 = 3).
What this means
Powers of the base
| Expression | Exponent | Result |
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Understanding exponents
What Are Exponents?
An exponent indicates how many times a base number is multiplied by itself. In the expression 2¹⁰, 2 is the base and 10 is the exponent. The result is 2 × 2 × 2 × ... (10 times) = 1,024. Exponents are also called powers or indices.
Rules of Exponents
Key exponent rules: a^m × a^n = a^(m+n), a^m / a^n = a^(m-n), (a^m)^n = a^(m×n), a^0 = 1 (for a ≠ 0), a^(-n) = 1/a^n. These rules simplify complex expressions and are fundamental in algebra, calculus, and computer science.
Negative and Fractional Exponents
A negative exponent means reciprocal: 2^(-3) = 1/2³ = 1/8 = 0.125. A fractional exponent means root: 8^(1/3) = ∛8 = 2, and 8^(2/3) = (∛8)² = 4. These extend the concept of exponents beyond simple repeated multiplication.
Exponents in Real Life
Exponents appear in compound interest (principal × (1+r)^n), population growth, radioactive decay, computer storage (2¹⁰ = 1 KB), earthquake magnitude (each step is 10×), and scientific notation (speed of light ≈ 3 × 10⁸ m/s).
Common questions
What is any number raised to the power of zero?
Any non-zero number raised to the power of zero equals 1. This follows from the rule a^n / a^n = a^(n-n) = a^0 = 1. The expression 0^0 is often considered undefined or defined as 1 by convention.
Can you raise a negative number to a fractional exponent?
It depends. Negative numbers can be raised to integer exponents. For fractional exponents, the result may be a complex number (e.g., (-1)^0.5 = i). This calculator handles real number results.
What is the difference between 2^10 and 10^2?
2^10 = 1,024 and 10^2 = 100. They are very different because the base and exponent play different roles. Changing which number is the base vs exponent dramatically changes the result.
How do exponents relate to logarithms?
Logarithms are the inverse of exponents. If 2^10 = 1024, then log₂(1024) = 10. They "undo" each other, similar to multiplication and division.
Results use JavaScript floating-point arithmetic (about 15-17 significant digits). Extremely large or small values are shown in scientific notation.