Exponent Rules

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

$$15x^5$$ .

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

$$3x^3$$ .

When raising a power to another power, multiply the exponents: $$(a^m)^n = a^{m \cdot n}$$ .

$$x^{36}$$ .

When raising a product to a power, apply the exponent to each factor: $$(ab)^n = a^n b^n$$ .

$$x^7$$ .

When raising a quotient to a power, apply the exponent to both the numerator and the denominator: $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$ .

$$x^9$$ .