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)

$= y^(5/3)$

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