Exponent Calculator
Evaluate powers, simplify exponential expressions, and apply exponent rules step-by-step.
Calculate Base to the Power of Exponent
Enter the base ($x$) and the exponent ($y$) to calculate $x^y$.
Laws and Rules of Exponents
Below is a quick reference guide for basic exponent rules:
| Rule Name | Rule Formula | Example |
|---|---|---|
| Product Rule | $a^m \cdot a^n = a^{m+n}$ | $2^3 \cdot 2^4 = 2^7 = 128$ |
| Quotient Rule | $\frac{a^m}{a^n} = a^{m-n}$ | $\frac{5^6}{5^2} = 5^4 = 625$ |
| Power Rule | $(a^m)^n = a^{m \cdot n}$ | $(3^2)^3 = 3^6 = 729$ |
| Power of a Product | $(ab)^n = a^n \cdot b^n$ | $(2 \cdot 4)^2 = 2^2 \cdot 4^2 = 64$ |
| Power of a Fraction | $(\frac{a}{b})^n = \frac{a^n}{b^n}$ | $(\frac{3}{2})^3 = \frac{27}{8} = 3.375$ |
| Zero Exponent Rule | $a^0 = 1 \quad (a \neq 0)$ | $7^0 = 1$ |
| Negative Exponent Rule | $a^{-n} = \frac{1}{a^n}$ | $2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125$ |
| Fractional Exponent Rule | $a^{\frac{m}{n}} = \sqrt[n]{a^m}$ | $8^{\frac{2}{3}} = \sqrt[3]{8^2} = 4$ |
Frequently Asked Questions (FAQs)
An exponent indicates how many times a base number is multiplied by itself. In $a^b$, $a$ is the base and $b$ is the exponent.
A negative exponent represents the reciprocal of the base raised to the positive power: $x^{-n} = \frac{1}{x^n}$.
According to the quotient rule, $\frac{a^n}{a^n} = a^{n-n} = a^0$. Since any number divided by itself equals 1, $a^0 = 1$.