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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

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

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

Simplify

((3 x)^{- \frac{2}{3}})^{2} : \frac{1}{3 \cdot 3 ^{\frac{1}{3}} x ^{\frac{4}{3}}}

= \frac{1}{9} \cdot \frac{1}{3 \cdot 3 ^{\frac{1}{3}} x ^{\frac{4}{3}}} \cdot 3^{2}

3^{2} = 9

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

Simplify

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

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

3^{1 + \frac{1}{3}} = 3 \cdot 3^{\frac{1}{3}}

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

z^{2} + ∣ z ∣ = 0

y^{2} - y - 6

(x - 6) (x - 2) = - 4

\frac{x}{4} \leq \frac{9}{x}

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