Question

How do you simplify `(z^(1/3))/(z^(-1/2)z^(1/4))`?

Answer 1

See full simplification process below:

Explanation:

First, simplify the denominator using the rule for exponents:

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

`(z^(1/3))/(z^(color(red)(-1/2))z^(color(blue)(1/4))) ->` `z^(1/3)/z^((color(red)(-1/2)+color(blue)(1/4))` `->` `(z^(1/3))/(z^((color(red)(-2/4)+color(blue)(1/4))` `->`

`z^(1/3)/z^(-1/4)`

Next, we can simplify the fraction using another rule for exponents:

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

`z^color(red)(1/3)/z^color(blue)(-1/4) = z^(color(red)(1/3)-color(blue)(-1/4)) = z^(color(red)(1/3)+color(blue)(1/4)) = z^(color(red)(4/12)+color(blue)(3/12)) = z^(color(red)(7/12)`