Question

How do you multiply and simplify `(y ^ { 4} \cdot z^\frac { 1} { 5} ) ^ { - \frac { 5} { 4} }`?

Answer 1

See the solution process below:

Explanation:

First, use this rule of exponents to begin the simplification process:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(y^color(red)(4)z^color(red)(1/5))^color(blue)(-5/4) = y^(color(red)(4) xx color(blue)(-5/4))z^(color(red)(1/5) xx color(blue)(-5/4)) = y^(-20/4)z^(-5/20) = y^-5z^(-1/4)`

Next, use this rule of exponents to eliminate the negative exponents:

`y^color(red)(-5)z^color(red)(--1/4) = 1/(y^color(red)(- -5a)z^color(red)(- -1/4)) = 1/(y^5z^(1/4)`