What is ((x^6y^{(-3)})/(8y^{3/2)})^{-1/3} ?

The solution to ((x^6y^{(-3)})/(8y^{3/2)})^{-1/3} is (2y^{3/2})/(x^2)

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simplify ((x^6y^{(-3)})/(8y^{3/2)})^{-1/3}

simplify

(\frac{x ^{6} y ^{(- 3)}}{8 y ^{\frac{3}{2}}})^{- \frac{1}{3}}

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

Solution steps

(\frac{x ^{6} y ^{- 3}}{8 y ^{\frac{3}{2}}})^{- \frac{1}{3}}

Apply exponent rule:

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

(\frac{x ^{6} y ^{- 3}}{8 y ^{\frac{3}{2}}})^{- \frac{1}{3}} = \frac{1}{( \frac{x ^{6} y ^{- 3}}{8 y ^{\frac{3}{2}}} ) ^{\frac{1}{3}}}

= \frac{1}{( \frac{x ^{6} y ^{- 3}}{8 y ^{\frac{3}{2}}} ) ^{\frac{1}{3}}}

Simplify

(\frac{x ^{6} y ^{- 3}}{8 y ^{\frac{3}{2}}})^{\frac{1}{3}} : \frac{x ^{2}}{2 y ^{\frac{3}{2}}}

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

Apply the fraction rule:

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

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

c^{2} + 9 c + 10 = - 2

3 x - 4 = x + 5

6 x^{2} + 31 x = 17

4 x (x + 5) - 3 (x + 5)

4 q < 8

What is ((x^6y^{(-3)})/(8y^{3/2)})^{-1/3} ?
The solution to ((x^6y^{(-3)})/(8y^{3/2)})^{-1/3} is (2y^{3/2})/(x^2)