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

The solution to ((x^{-2}y^3)/(x^2y))^{-1/2}((x^3y)/(y^{1/2)})^2 is x^8

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

simplify

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

x^{8}

Solution steps

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

Simplify

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

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

Simplify

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

= \frac{x ^{2}}{y} x^{6} y

Cross-cancel common factor:

y

= x^{2} x^{6}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x^{2} x^{6} = x^{2 + 6}

= x^{2 + 6}

Add the numbers:

2 + 6 = 8

= x^{8}

\frac{2 x ^{2} y ^{4} \cdot 4 x ^{2} y ^{4} \cdot 3 x}{3 x ^{- 3} y ^{2}}

2 x^{2} + 10 x + 11 = 0

\frac{4}{5} x = - 2

lo g_{4} (5) x^{2} + lo g_{4} (5) = 1

2 a^{0}

What is ((x^{-2}y^3)/(x^2y))^{-1/2}((x^3y)/(y^{1/2)})^2 ?
The solution to ((x^{-2}y^3)/(x^2y))^{-1/2}((x^3y)/(y^{1/2)})^2 is x^8