What is (3x^2)^{-3}*(x^9)^{2/3} ?

The solution to (3x^2)^{-3}*(x^9)^{2/3} is 1/27

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simplify (3x^2)^{-3}*(x^9)^{2/3}

simplify

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

\frac{1}{27}

Solution steps

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

Simplify

(3 x^{2})^{- 3} : \frac{1}{27 x ^{6}}

= \frac{1}{27 x ^{6}} (x^{9})^{\frac{2}{3}}

Simplify

(x^{9})^{\frac{2}{3}} : x^{6}

= \frac{1}{27 x ^{6}} x^{6}

Apply the fraction rule:

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

= \frac{1 \cdot x ^{6}}{27 x ^{6}}

Apply rule:

1 \cdot a = a

1 \cdot x^{6} = x^{6}

= \frac{x ^{6}}{27 x ^{6}}

Cancel the common factor:

x^{6}

= \frac{1}{27}

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y \cdot z^{2} \cdot x^{2} + x^{2} \cdot y^{2} \cdot z + x^{2} \cdot y + x^{2} \cdot z

2 x^{3} + 5 x^{2} y - 12 x y^{2}

What is (3x^2)^{-3}*(x^9)^{2/3} ?
The solution to (3x^2)^{-3}*(x^9)^{2/3} is 1/27