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Popular >

simplify (sqrt(1+e^{2x)})^3

Solution

simplify

(1 + e^{2 x})^{3}

Solution

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

Solution steps

(1 + e^{2 x})^{3}

Apply radical rule:

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

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

Apply exponent rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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