How do you simplify #(y*y^(1/4))^(4/3))#?

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Answer 1 · 2017-01-15T07:36:28

#y^(5/3)#

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

Recall two rules indices as follows:

(i) #a^m xx a^n = a^(m+n)#

(ii) #(a^m)^n = a^(m xx n)#

Applying both rules to our expression:

#(y^1*y^(1/4))^(4/3) = (y^(1+1/4))^(4/3) = (y^(5/4))^(4/3)# Rule (i)

#= y^(5/4 xx 4/3)# Rule (ii)

#= y^(5/3)#