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

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

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

expand

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

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

Solution steps

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

(- \frac{1}{2}) \cdot 3 = - \frac{3}{2}

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

Apply exponent rule:

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

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

(8 y^{3} sec^{2} (2 x) + 4 x^{3} e^{-} 3 y + 6 csc^{2} (3 x)) d x

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14.944 \cdot (x^{2}) \cdot (\frac{2}{3} x + 6.75)

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