What is ((x^2)/(x^{-11)})^{1/3} ?

The solution to ((x^2)/(x^{-11)})^{1/3} is x^{13/3}

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simplify ((x^2)/(x^{-11)})^{1/3}

simplify

(\frac{x ^{2}}{x ^{- 11}})^{\frac{1}{3}}

x^{\frac{13}{3}}

Solution steps

(\frac{x ^{2}}{x ^{- 11}})^{\frac{1}{3}}

Apply exponent rule:

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

= \frac{( x ^{2} ) ^{\frac{1}{3}}}{( x ^{- 11} ) ^{\frac{1}{3}}}

Simplify

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

= \frac{x ^{\frac{2}{3}}}{( x ^{- 11} ) ^{\frac{1}{3}}}

Simplify

(x^{- 11})^{\frac{1}{3}} : \frac{1}{x ^{\frac{11}{3}}}

= \frac{x ^{\frac{2}{3}}}{\frac{1}{x ^{\frac{11}{3}}}}

Apply the fraction rule:

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

= \frac{x ^{\frac{2}{3}} x ^{\frac{11}{3}}}{1}

Apply rule

\frac{a}{1} = a

= x^{\frac{11}{3}} x^{\frac{2}{3}}

Apply exponent rule:

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

x^{\frac{2}{3}} x^{\frac{11}{3}} = x^{\frac{2}{3} + \frac{11}{3}}

= x^{\frac{2}{3} + \frac{11}{3}}

Join

\frac{2}{3} + \frac{11}{3} : \frac{13}{3}

= x^{\frac{13}{3}}

19 = 14 + k

x^{3} - 27 x

(2 x + 1) (x + 3) = - 1

x (x - 2) > 0

\frac{1}{8} + \frac{1}{2}

What is ((x^2)/(x^{-11)})^{1/3} ?
The solution to ((x^2)/(x^{-11)})^{1/3} is x^{13/3}