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

1 Answer
Jan 11, 2017

Answer:

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)#