How do you simplify #((x^(1/2)y^-2)/(yx^(7/4)))^4#?

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Answer 1 · 2017-08-26T16:22:06

#1/(x^5 y^12)#

#((x^(1/2) y^-2)/(y x^(7/4)))^4#

#((x^(1/2 xx 4) y^(-2 xx 4))/(y^4 x^(7/4 xx 4)))#

#((x^2 y^-8)/(y^4 x^7))#

#x^2 y^-8 div y^4 x^7#

Recall

#a^x xx a^y = a^(x+y)#

#a^x div a^y = a^(x-y)#

#rArr x^(2 - 7) y^(-8 - 4)#

#rArr x^-5 y^-12#

#rArr 1/(x^5 y^12)#