What is (-2x^2)^3(4x^3)^{-1} ?

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

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simplify (-2x^2)^3(4x^3)^{-1}

simplify

(- 2 x^{2})^{3} (4 x^{3})^{- 1}

- 2 x^{3}

Solution steps

(- 2 x^{2})^{3} (4 x^{3})^{- 1}

Simplify

(- 2 x^{2})^{3} : - 8 x^{6}

= - 8 x^{6} (4 x^{3})^{- 1}

Apply exponent rule:

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

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

= - 8 x^{6} \frac{1}{4 x ^{3}}

Apply the fraction rule:

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

= - \frac{8 x ^{6} \cdot 1}{4 x ^{3}}

Multiply the numbers:

8 \cdot 1 = 8

= - \frac{8 x ^{6}}{4 x ^{3}}

Factor the number:

8 = 4 \cdot 2

= - \frac{4 \cdot 2 x ^{6}}{4 x ^{3}}

Cancel the common factor:

4

= - \frac{2 x ^{6}}{x ^{3}}

Simplify

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

= - 2 x^{3}

9 x - 2 + 3 x - 5

(\frac{1}{2} - 3 a)^{4}

- ∣ 15 ∣

16 x^{2} - 8 x + 1

- 0.8 (3 x - 31) + 5.5