What is ((9x^3y)/(y^{-3)})^{1/2} ?

The solution to ((9x^3y)/(y^{-3)})^{1/2} is 3y^2x^{3/2}

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simplify ((9x^3y)/(y^{-3)})^{1/2}

simplify

(\frac{9 x ^{3} y}{y ^{- 3}})^{\frac{1}{2}}

3 y^{2} x^{\frac{3}{2}}

Solution steps

(\frac{9 x ^{3} y}{y ^{- 3}})^{\frac{1}{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 9 x ^{3} y ) ^{\frac{1}{2}}}{( y ^{- 3} ) ^{\frac{1}{2}}}

Simplify

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

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

Simplify

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

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

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

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

Apply rule

\frac{a}{1} = a

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

Apply exponent rule:

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

y^{\frac{1}{2}} y^{\frac{3}{2}} = y^{\frac{1}{2} + \frac{3}{2}}

= 3 x^{\frac{3}{2}} y^{\frac{1}{2} + \frac{3}{2}}

y^{\frac{1}{2} + \frac{3}{2}} = y^{2}

= 3 y^{2} x^{\frac{3}{2}}

6 x^{2} + 12 x - 27

x^{2} + 18 x + 72

\frac{32 x ^{3} y ^{2} z ^{5}}{- 8 x y z ^{2}}

(x - 1)^{2} - 9 = 0

\frac{7}{12} + \frac{5}{6}

What is ((9x^3y)/(y^{-3)})^{1/2} ?
The solution to ((9x^3y)/(y^{-3)})^{1/2} is 3y^2x^{3/2}