What is (x^{1/2}y^{-2/3})^{-6} ?

The solution to (x^{1/2}y^{-2/3})^{-6} is (y^4)/(x^3)

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simplify (x^{1/2}y^{-2/3})^{-6}

simplify

(x^{\frac{1}{2}} y^{- \frac{2}{3}})^{- 6}

\frac{y ^{4}}{x ^{3}}

Solution steps

(x^{\frac{1}{2}} y^{- \frac{2}{3}})^{- 6}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(x^{\frac{1}{2}} y^{- \frac{2}{3}})^{- 6} = \frac{1}{( x ^{\frac{1}{2}} y ^{- \frac{2}{3}} ) ^{6}}

= \frac{1}{( x ^{\frac{1}{2}} y ^{- \frac{2}{3}} ) ^{6}}

Simplify

(x^{\frac{1}{2}} y^{- \frac{2}{3}})^{6} : \frac{x ^{3}}{y ^{4}}

= \frac{1}{\frac{x ^{3}}{y ^{4}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{y ^{4}}{x ^{3}}

x^{2} + 2 x - 19 = 0

2 x^{3} - 5 x^{2} + 4 x - 10

10 x^{2} - 19 x - 15

- 5 x - 7 = 108

\frac{x - 9}{21} = \frac{6}{7} - \frac{x - 7}{14}

What is (x^{1/2}y^{-2/3})^{-6} ?
The solution to (x^{1/2}y^{-2/3})^{-6} is (y^4)/(x^3)