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

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

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

expand

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

\frac{x ^{4}}{( 2 x ^{4} - 1 ) ^{4}}

Solution steps

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

Apply exponent rule:

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

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

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

= \frac{1}{\frac{( 2 x ^{4} - 1 ) ^{4}}{x ^{4}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{x ^{4}}{( 2 x ^{4} - 1 ) ^{4}}

v^{- 4} cos (v)

4^{3} e^{- 4}

e^{- 7} \frac{7 ^{6}}{6 !}

e^{x} sin (x) e^{x} sin (x)

What is expand (2x^3-1/x)^{-4} ?
The solution to expand (2x^3-1/x)^{-4} is (x^4)/((2x^4-1)^4)