Question

How do you simplify `(\frac { x ^ { 2} y ^ { - 3} } { z ^ { - 2} } ) ^ { 2}`?

Answer 1

See the entire simplification process below:

Explanation:

First, use this rule of exponents: `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`((x^color(red)(2)y^color(red)(-3))/z^color(red)(-2))^color(blue)(2) = (x^(color(red)(2)xxcolor(blue)(2))y^(color(red)(-3)xxcolor(blue)(2)))/z^(color(red)(-2)xxcolor(blue)(2)) = (x^4y^-6)/z^-4`

To remove the negative exponents use these rules for exponents:

`x^color(red)(a) = 1/x^color(red)(-a)` and `1/x^color(red)(a) = x^color(red)(-a)`

`(x^4y^color(red)(-6))/z^color(red)(-4) = (x^4z^color(red)(- -4))/y^color(red)(- -6) = (x^4z^4)/y^6`