Exponent Rules!

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

When dividing powers 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: $$(a^m)^n = a^{m \times n}$$ .

Any non-zero number raised to the zero power is equal to 1: $$a^0 = 1$$ .

When multiplying powers with different bases but the same exponent, multiply the bases and keep the exponent: $$a^n \times b^n = (a \times b)^n$$ .

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

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

$$x^{5-2} = x^3$$ .

$$2^2 \times (x^3)^2 = 4x^{6}$$ .

$$3^2 = 9$$ .