What is ((sqrt(x^5))/(x^{-2)})^{1/3} ?

The solution to ((sqrt(x^5))/(x^{-2)})^{1/3} is x^{3/2}

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simplify ((sqrt(x^5))/(x^{-2)})^{1/3}

simplify

(\frac{x ^{5}}{x ^{- 2}})^{\frac{1}{3}}

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

Solution steps

(\frac{x ^{5}}{x ^{- 2}})^{\frac{1}{3}}

Apply exponent rule:

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

= \frac{( x ^{5} ) ^{\frac{1}{3}}}{( x ^{- 2} ) ^{\frac{1}{3}}}

Simplify

(x^{5})^{\frac{1}{3}} : x^{\frac{5}{6}}

= \frac{x ^{\frac{5}{6}}}{( x ^{- 2} ) ^{\frac{1}{3}}}

Simplify

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

= \frac{x ^{\frac{5}{6}}}{\frac{1}{x ^{\frac{2}{3}}}}

Apply the fraction rule:

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

= \frac{x ^{\frac{5}{6}} x ^{\frac{2}{3}}}{1}

Apply rule

\frac{a}{1} = a

= x^{\frac{5}{6}} x^{\frac{2}{3}}

Apply exponent rule:

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

x^{\frac{5}{6}} x^{\frac{2}{3}} = x^{\frac{5}{6} + \frac{2}{3}}

= x^{\frac{5}{6} + \frac{2}{3}}

Join

\frac{5}{6} + \frac{2}{3} : \frac{3}{2}

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

\frac{x ^{\frac{5}{2}}}{x ^{\frac{3}{2}}}

- x^{3} - x^{2}

x^{3} + 10 x^{2} + 31 x + 30

- 8 (- 2.8 + 1.2)

What is ((sqrt(x^5))/(x^{-2)})^{1/3} ?
The solution to ((sqrt(x^5))/(x^{-2)})^{1/3} is x^{3/2}