Question

Simplify the following leaving your answer in positive index

1) (x/y)^-4 x (y/x)^8

Answer 1

Answer:

$(\frac{x}{y})^{-4} * (\frac{y}{x})^8 = (\frac{y}{x})^{12$

Step-by-step explanation:

Given

$(\frac{x}{y})^{-4} * (\frac{y}{x})^8$

Required

Determine the solution to this

$(\frac{x}{y})^{-4} * (\frac{y}{x})^8$

In law of incides:

$\frac{a}{b} = \frac{b}{a}^{-1}$

This implies that:

$(\frac{x}{y})^{-4} * (\frac{y}{x})^8$ is equivalent to:

$(\frac{y}{x})^{-(-4)} * (\frac{y}{x})^8$

$(\frac{y}{x})^{4} * (\frac{y}{x})^8$

Apply first law of indices:

$(\frac{y}{x})^{4+8$

$(\frac{y}{x})^{12$

Hence:

$(\frac{x}{y})^{-4} * (\frac{y}{x})^8 = (\frac{y}{x})^{12$