What is ((e^*(2x)^3))/((e^{4x^2))} ?

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

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simplify ((e^*(2x)^3))/((e^{4x^2))}

simplify

\frac{( e ^{\cdot} ( 2 x ) ^{3} )}{( e ^{4 x^{2}} )}

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

Solution steps

\frac{e ( 2 x ) ^{3}}{e ^{4 x^{2}}}

Apply exponent rule:

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

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

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

(2 x)^{3} = 2^{3} x^{3}

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

2^{3} = 8

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

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

\frac{4 \times ( \frac{100}{10} )}{28 + 15}

\frac{y ^{3}}{y ^{- 2}}

4 x^{2} - 8 x y^{2} + 10 x^{2} y^{2}

∣ x + y ∣^{2} + ∣ x - y ∣^{2}

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