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# How do you simplify (3x^(-1/2)*3x^(1/2)y^(-1/3))/(3y^(-7/4))?

How do you simplify (3x^(-1/2)*3x^(1/2)y^(-1/3))/(3y^(-7/4))?

Answer 1

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$3 {y}^{\frac{17}{12}}$

#### Explanation:

(3x^(-1/2)*3x^(1/2)y^(-1/3))/(3y^(-7/4)

$\therefore = \frac{9 {x}^{- \frac{1}{2} + \frac{1}{2}} \cdot {y}^{- \frac{1}{3}}}{3 {y}^{- \frac{7}{4}}}$

$\therefore = \frac{{\cancel{9}}^{\textcolor{b l u e}{3}} {x}^{0} \cdot {y}^{- \frac{1}{3}}}{{\cancel{3}}^{\textcolor{b l u e}{1}} {y}^{- \frac{7}{4}}}$

$\therefore = \frac{3 \cdot 1 \cdot {y}^{- \frac{1}{3}}}{y} ^ \left(- \frac{7}{4}\right)$

$\therefore = \frac{3}{y} ^ \left(- \frac{7}{4} + \frac{1}{3}\right)$

:.=color(blue)(3/(y^(-17/12) $\textcolor{w h i t e}{a a a a a a a a a a a a a}$ -7/4+1/3=(-21+4)/12=color(blue)(-17/12

answered by: Barney V.
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