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

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Answer 1 · 2016-09-17T11:42:40

$\frac{20^{20} \times 6 y^{2}}{x^{3}}$ $(20^20 xx6y^2)/x^3$

${[{(\frac{x^{2}}{5} \frac{y^{3}}{4})}^{5}]}^{- 4} {(36 x^{- 6} y^{4})}^{\frac{1}{2}}$ $[(x^2/5y^3/4)^5]^-4 (36x^-6y^4)^(1/2)$

Remove the outer brackets by multiplying the indices, to give

= ${(\frac{x^{2}}{5} \frac{y^{3}}{4})}^{- 20} \times 36^{\frac{1}{2}} x^{- 3} y^{2}$ $(x^2/5y^3/4)^-20 xx36^(1/2)x^-3y^2$

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Recall: two laws for negative indices and $x^{\frac{1}{2}} = \sqrt{x}$ $x^(1/2) = sqrtx$

${(\frac{a}{b})}^{- m} = {(\frac{b}{a})}^{m} and x^{- m} = \frac{1}{x^{m}}$ $(a/b)^-m = (b/a)^m" and " x^-m = 1/x^m$

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${(\frac{5}{x^{2}} \frac{4}{y^{3}})}^{20} \times \frac{\sqrt{36} \times y^{2}}{x^{3}}$ $(5/x^2 4/y^3)^20 xx (sqrt36xxy^2)/x^3$

= $20^{20} \times 6 \frac{y^{2}}{x^{3}}$ $20^20 xx 6y^2/x^3$

= $\frac{20^{20} \times 6 y^{2}}{x^{3}}$ $(20^20 xx6y^2)/x^3$

How do you simplify and write [(x25y34)5]−4(36x−6y4)12[(x^2/5y^3/4)^5]^-4 (36x^-6y^4)^(1/2) with positive exponents?