What is (-3x^2)^5(9x^3)^{-1} ?

The solution to (-3x^2)^5(9x^3)^{-1} is -27x^7

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simplify (-3x^2)^5(9x^3)^{-1}

simplify

(- 3 x^{2})^{5} (9 x^{3})^{- 1}

- 27 x^{7}

Solution steps

(- 3 x^{2})^{5} (9 x^{3})^{- 1}

Simplify

(- 3 x^{2})^{5} : - 243 x^{10}

= - 243 x^{10} (9 x^{3})^{- 1}

Apply exponent rule:

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

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

= - 243 x^{10} \frac{1}{9 x ^{3}}

Apply the fraction rule:

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

= - \frac{243 x ^{10} \cdot 1}{9 x ^{3}}

Multiply the numbers:

243 \cdot 1 = 243

= - \frac{243 x ^{10}}{9 x ^{3}}

Factor the number:

243 = 9 \cdot 27

= - \frac{9 \cdot 27 x ^{10}}{9 x ^{3}}

Cancel the common factor:

9

= - \frac{27 x ^{10}}{x ^{3}}

Simplify

\frac{x ^{10}}{x ^{3}} : x^{7}

= - 27 x^{7}

\frac{2}{x + 2} + \frac{3}{x + 3}

\frac{b ^{- 17} b ^{11}}{b ^{- 5}}

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

(x + 1)^{2} + (x - 2)^{2}

\frac{3 x}{6}