Question

1. $x^{-4}y^{2}cdot (x^{-2}y^{-2})^{2}$

Explanation:

Step1: Apply power of a product rule

$(x^{-2}y^{-2})^2 = x^{-2\times2}y^{-2\times2} = x^{-4}y^{-4}$

Step2: Multiply like terms with exponents

$x^{-4}y^{2} \cdot x^{-4}y^{-4} = x^{-4+(-4)}y^{2+(-4)}$

Step3: Simplify the exponents

$x^{-8}y^{-2} = \frac{1}{x^8y^2}$

Answer:

$\frac{1}{x^8y^2}$