What is (3x^{-1/2}*3x^{1/2}y^{-1/3})/(3y^{-7/4)} ?

The solution to (3x^{-1/2}*3x^{1/2}y^{-1/3})/(3y^{-7/4)} is 3y^{17/12}

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

simplify

\frac{3 x ^{- \frac{1}{2}} \cdot 3 x ^{\frac{1}{2}} y ^{- \frac{1}{3}}}{3 y ^{- \frac{7}{4}}}

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

Solution steps

\frac{3 x ^{- \frac{1}{2}} \cdot 3 x ^{\frac{1}{2}} y ^{- \frac{1}{3}}}{3 y ^{- \frac{7}{4}}}

Cancel the common factor:

3

= \frac{3 x ^{- \frac{1}{2}} x ^{\frac{1}{2}} y ^{- \frac{1}{3}}}{y ^{- \frac{7}{4}}}

Simplify

\frac{y ^{- \frac{1}{3}}}{y ^{- \frac{7}{4}}} : y^{\frac{17}{12}}

= 3 x^{- \frac{1}{2}} x^{\frac{1}{2}} y^{\frac{17}{12}}

Simplify

3 x^{- \frac{1}{2}} x^{\frac{1}{2}} y^{\frac{17}{12}} : 3 y^{\frac{17}{12}}

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

500 \leq \frac{( x + 1 ) ^{2}}{4} \leq 1000

x^{3} + 4 x^{2} + 4 x + 16

\frac{x}{7} + 4 = - 5

2.2 m < 11

(241 x) \cdot 9995 = 1.0 E 32

What is (3x^{-1/2}*3x^{1/2}y^{-1/3})/(3y^{-7/4)} ?
The solution to (3x^{-1/2}*3x^{1/2}y^{-1/3})/(3y^{-7/4)} is 3y^{17/12}