Exponent Product and Power Rules

The Exponent Product Rule states that when multiplying two expressions with the same base, you add the exponents. For example, $$a^m \times a^n = a^{m+n}$$ .

The Exponent Power Rule states that when raising a power to another power, you multiply the exponents. For example, $$(a^m)^n = a^{m \times n}$$ .

Using the Exponent Product Rule, $$x^2 \times x^5 = x^{2+5} = x^7$$ .

Using the Exponent Power Rule, $$(y^3)^4 = y^{3 \times 4} = y^{12}$$ .

Using the Exponent Product Rule, $$2^3 \times 2^2 = 2^{3+2} = 2^5 = 32$$ .

Using the Exponent Power Rule, $$(3^2)^3 = 3^{2 \times 3} = 3^6 = 729$$ .

Using the Exponent Product Rule, $$x = 4 + 3 = 7$$ .

Using the Exponent Power Rule, $$y = 5 \times 2 = 10$$ .

For any non-zero number, $$x^0 = 1$$ .

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