What is (-4x^3)^2*(8x^4)^{-1} ?

The solution to (-4x^3)^2*(8x^4)^{-1} is 2x^2

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simplify (-4x^3)^2*(8x^4)^{-1}

simplify

(- 4 x^{3})^{2} \cdot (8 x^{4})^{- 1}

2 x^{2}

Solution steps

(- 4 x^{3})^{2} (8 x^{4})^{- 1}

Simplify

(- 4 x^{3})^{2} : 16 x^{6}

= 16 x^{6} (8 x^{4})^{- 1}

Apply exponent rule:

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

(8 x^{4})^{- 1} = \frac{1}{8 x ^{4}}

= 16 x^{6} \frac{1}{8 x ^{4}}

Apply the fraction rule:

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

= \frac{16 x ^{6} \cdot 1}{8 x ^{4}}

Multiply the numbers:

16 \cdot 1 = 16

= \frac{16 x ^{6}}{8 x ^{4}}

Factor the number:

16 = 8 \cdot 2

= \frac{8 \cdot 2 x ^{6}}{8 x ^{4}}

Cancel the common factor:

8

= \frac{2 x ^{6}}{x ^{4}}

Simplify

\frac{x ^{6}}{x ^{4}} : x^{2}

= 2 x^{2}

(p^{- 1} + q^{- 1})^{- 1}

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\frac{1 + tan ^{2} ( x )}{cos ^{2} ( x )}