4) simplify. x^5y^(-2)/x^7y^4

Explanation:

Step1: Use exponent - division rule

When dividing like - bases $a^m\div a^n=a^{m - n}$, for the $x$ terms: $x^5\div x^7=x^{5 - 7}$, and for the $y$ terms: $y^{-2}\div y^4=y^{-2-4}$.

Step2: Calculate the exponents

$x^{5 - 7}=x^{-2}$ and $y^{-2 - 4}=y^{-6}$.

Step3: Rewrite with positive exponents

Recall that $a^{-n}=\frac{1}{a^n}$, so $x^{-2}=\frac{1}{x^2}$ and $y^{-6}=\frac{1}{y^6}$. Then the expression becomes $\frac{1}{x^2y^6}$.

Answer:

$\frac{1}{x^2y^6}$