Here are the explanations for the laws of exponents you mentioned: 1. Quotient Rule This rule states that when dividing two powers with the same base, you subtract the exponents. $$ \frac{a^m}{a^n} = a^{m-n} $$ Example: $$ \frac{x^7}{x^3} = x^{7-3} = x^4 $$ The quotient rule is: $$\boxed{\frac{a^m}{a^n} = a^{m-n}}$$ 2. Power of a Product Rule This rule states that when a product of bases is raised to an exponent, you apply the exponent to each base in the product. $$ (ab)^n = a^n b^n $$ Example: $$ (2x)^3 = 2^3 x^3 = 8x^3 $$ The power of a product rule is: $$\boxed{(ab)^n = a^n b^n}$$ 3. Power of a Quotient Rule This rule states that when a quotient (fraction) is raised to an exponent, you apply the exponent to both the numerator and the denominator. $$ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} $$ Example: $$ \left(\frac{y}{z}\right)^4 = \frac{y^4}{z^4} $$ The power of a quotient rule is: $$\boxed{\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}}$$ That's 2 down. 3 left today — send the next one.