What is (sqrt(4e^{-4x)+4})^3 ?

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

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simplify (sqrt(4e^{-4x)+4})^3

simplify

(4 e^{- 4 x} + 4)^{3}

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

Solution steps

(4 e^{- 4 x} + 4)^{3}

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

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

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

\frac{1}{2} \cdot 3 = \frac{3}{2}

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

Factor

4 e^{- 4 x} + 4 : 4 (e^{- 4 x} + 1)

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

4^{\frac{3}{2}} = 8

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

18 e^{- 0.2 (5)}

e^{x} \times 2 e^{2 x} \times 9 e^{3 x}

3 e^{- 7 t}

3 x^{2} \times (2 x^{3})

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