Question

1. $x^{2}y^{-4} \cdot x^{3}y^{2}$

Explanation:

Step1: Group like variables

Group the $x$-terms and $y$-terms separately.
$x^2 \cdot x^3 \cdot y^{-4} \cdot y^2$

Step2: Apply exponent product rule

For same bases, add exponents: $a^m \cdot a^n = a^{m+n}$.
$x^{2+3} \cdot y^{-4+2}$

Step3: Simplify exponents

Calculate the sums of the exponents.
$x^{5} \cdot y^{-2}$

Step4: Rewrite negative exponent

Use $a^{-n}=\frac{1}{a^n}$ to make exponent positive.
$x^5 \cdot \frac{1}{y^2} = \frac{x^5}{y^2}$

Answer:

$\frac{x^5}{y^2}$