Exponent Rules

When multiplying two powers with the same base, you add the exponents. For example, $$a^m \times a^n = a^{m+n}$$ .

When dividing two powers with the same base, you subtract the exponents. For example, $$\frac{a^m}{a^n} = a^{m-n}$$ .

When raising a power to another power, you multiply the exponents. For example, $$(a^m)^n = a^{m \times n}$$ .

When raising a product to a power, you apply the exponent to each factor. For example, $$(ab)^n = a^n \times b^n$$ .

When raising a quotient to a power, you apply the exponent to both the numerator and the denominator. For example, $$\frac{a}{b}^n = \frac{a^n}{b^n}$$ .

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, $$a^{-n} = \frac{1}{a^n}$$ .

$$(-2)^9$$ .

$$x^2$$ .

Zero raised to any positive power is zero. However, zero raised to the power of zero is undefined.

$$x^0 = 1$$ for any non-zero x.