What is (sqrt(100e^{20x)+e^{-2x}})^3 ?

The solution to (sqrt(100e^{20x)+e^{-2x}})^3 is (100e^{20x}+e^{-2x})^{3/2}

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simplify (sqrt(100e^{20x)+e^{-2x}})^3

simplify

(100 e^{20 x} + e^{- 2 x})^{3}

(100 e^{20 x} + e^{- 2 x})^{\frac{3}{2}}

Solution steps

(100 e^{20 x} + e^{- 2 x})^{3}

Apply radical rule:

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

= ((100 e^{20 x} + e^{- 2 x})^{\frac{1}{2}})^{3}

Apply exponent rule:

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

= (100 e^{20 x} + e^{- 2 x})^{\frac{1}{2} \cdot 3}

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

= (100 e^{20 x} + e^{- 2 x})^{\frac{3}{2}}

10 e^{- \frac{1}{( 108 \cdot 0.002 )}}

(2.25 \cdot 1 0^{- 2}) ((0.28)^{2})

e^{- \frac{1}{x} d x}

\frac{d}{d x} (x^{2} + y^{2} + z^{2})

What is (sqrt(100e^{20x)+e^{-2x}})^3 ?
The solution to (sqrt(100e^{20x)+e^{-2x}})^3 is (100e^{20x}+e^{-2x})^{3/2}