Question

How do you divide `\frac { z ^ { 3} } { ( z ^ { 3} ) ^ { 5} }`?

Answer 1

See a solution process below:

Explanation:

First, use this rule for exponents to simplify the denominator:

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

`z^3/(z^color(red)(3))^color(blue)(5) => z^3/z^(color(red)(3) xx color(blue)(5)) => z^3/z^15`

Now, use this rule of exponents to complete the division:

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

`z^color(red)(3)/z^color(blue)(15) => 1/z^(color(blue)(15)-color(red)(3)) => 1/z^12`