Exponent Rules

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

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

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

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

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

$$x^7$$ .

$$m^5$$ .

$$\frac{y^{12}}{3^4x^{20}}$$ .

$$\frac{1}{x^{\frac{7}{5}}}$$ .

$$4^5$$ .