How do you simplify #(\frac { 81x ^ { 2} } { y } ) ^ { \frac { 3} { 4} }#?

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Answer 1 · 2017-12-10T11:01:52

#27x^(3/2) y^(-3/4) # or #(27 sqrt (x^3))/root4 (y^3) #

The first thing to consider is that:

# ((81x^2)/y)^(3/4) = ((81^(3/4))*(x^2)^(3/4))/(y^(3/4)) #

#81^(3/4) = root4 (81^3) = 3^3 = 27 #

#(x^2)^(3/4) = x^(2*(3/4)) = x^(3/2) = sqrt (x^3) #

#y^(3/4) = root4 (y^3) #

# 1/y^(3/4) = y^(-3/4) #

#=> 27x^(3/2)y^(-3/4) # or #(27 sqrt (x^3))/root4 (y^3) #