How do you simplify ${(\frac{x^{\frac{1}{2}} y^{- 2}}{y x^{\frac{7}{4}}})}^{4}$ $((x^(1/2)y^-2)/(yx^(7/4)))^4$ ?

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Answer 1 · 2017-08-26T16:22:06

$\frac{1}{x^{5} y^{12}}$ $1/(x^5 y^12)$

${(\frac{x^{\frac{1}{2}} y^{- 2}}{y x^{\frac{7}{4}}})}^{4}$ $((x^(1/2) y^-2)/(y x^(7/4)))^4$

$(\frac{x^{\frac{1}{2} \times 4} y^{- 2 \times 4}}{y^{4} x^{\frac{7}{4} \times 4}})$ $((x^(1/2 xx 4) y^(-2 xx 4))/(y^4 x^(7/4 xx 4)))$

$(\frac{x^{2} y^{- 8}}{y^{4} x^{7}})$ $((x^2 y^-8)/(y^4 x^7))$

$x^{2} y^{- 8} \div y^{4} x^{7}$ $x^2 y^-8 div y^4 x^7$

Recall

$a^{x} \times a^{y} = a^{x + y}$ $a^x xx a^y = a^(x+y)$

$a^{x} \div a^{y} = a^{x - y}$ $a^x div a^y = a^(x-y)$

$\Rightarrow x^{2 - 7} y^{- 8 - 4}$ $rArr x^(2 - 7) y^(-8 - 4)$

$\Rightarrow x^{- 5} y^{- 12}$ $rArr x^-5 y^-12$

$\Rightarrow \frac{1}{x^{5} y^{12}}$ $rArr 1/(x^5 y^12)$

How do you simplify (x12y−2yx74)4((x^(1/2)y^-2)/(yx^(7/4)))^4?