How do you simplify and write #[(x^2/5y^3/4)^5]^-4 (36x^-6y^4)^(1/2)# with positive exponents?

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Answer 1 · 2016-09-17T11:42:40

#(20^20 xx6y^2)/x^3#

#[(x^2/5y^3/4)^5]^-4 (36x^-6y^4)^(1/2)#

Remove the outer brackets by multiplying the indices, to give

=#(x^2/5y^3/4)^-20 xx36^(1/2)x^-3y^2#

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Recall: two laws for negative indices and #x^(1/2) = sqrtx#

#(a/b)^-m = (b/a)^m" and " x^-m = 1/x^m#

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#(5/x^2 4/y^3)^20 xx (sqrt36xxy^2)/x^3#

=#20^20 xx 6y^2/x^3#

=#(20^20 xx6y^2)/x^3#