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Popular >

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

Solution

simplify

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

Solution

\frac{1}{9 x ^{\frac{4}{3}}}

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

(\frac{1}{3})^{2} = \frac{1}{9}

= \frac{1}{9} (x^{- \frac{2}{3}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

= \frac{1}{9} x^{- \frac{2}{3} \cdot 2}

- \frac{2}{3} \cdot 2 = - \frac{4}{3}

= \frac{1}{9} x^{- \frac{4}{3}}

Apply exponent rule:

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

x^{- \frac{4}{3}} = \frac{1}{x ^{\frac{4}{3}}}

= \frac{1}{9} \cdot \frac{1}{x ^{\frac{4}{3}}}

Simplify

\frac{1}{9} \cdot \frac{1}{x ^{\frac{4}{3}}} : \frac{1}{9 x ^{\frac{4}{3}}}

= \frac{1}{9 x ^{\frac{4}{3}}}

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Frequently Asked Questions (FAQ)

What is (1/3 x^{-2/3})^2 ?
The solution to (1/3 x^{-2/3})^2 is 1/(9x^{4/3)}