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

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

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

simplify

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

3^{\frac{2}{3}} e^{2 x}

Solution steps

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

Apply exponent rule:

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

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

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

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

Combine the fractions

\frac{2}{3} + \frac{4}{3} : 2

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

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

= 3^{\frac{2}{3}} e^{2 x}

11 e^{- 0.05 \cdot \frac{6}{12}}

26.79 \cdot 1 0^{- 8}

0.35 e^{- 0.019803}

2.26 \cdot 1 0^{- 3}

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