What is (-3x^2)^3(9x^3)^{-1} ?

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

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simplify (-3x^2)^3(9x^3)^{-1}

simplify

(- 3 x^{2})^{3} (9 x^{3})^{- 1}

- 3 x^{3}

Solution steps

(- 3 x^{2})^{3} (9 x^{3})^{- 1}

Simplify

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

= - 27 x^{6} (9 x^{3})^{- 1}

Apply exponent rule:

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

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

= - 27 x^{6} \frac{1}{9 x ^{3}}

Apply the fraction rule:

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

= - \frac{27 x ^{6} \cdot 1}{9 x ^{3}}

Multiply the numbers:

27 \cdot 1 = 27

= - \frac{27 x ^{6}}{9 x ^{3}}

Factor the number:

27 = 9 \cdot 3

= - \frac{9 \cdot 3 x ^{6}}{9 x ^{3}}

Cancel the common factor:

9

= - \frac{3 x ^{6}}{x ^{3}}

Simplify

\frac{x ^{6}}{x ^{3}} : x^{3}

= - 3 x^{3}

\frac{5 ^{- 2}}{5 ^{4}}

\frac{3 a ^{2} b ^{3}}{9 ab}

2 - 1 \frac{1}{2}

- \frac{4 ^{2}}{4} + 7

2 x^{2} - 32 x^{4}