What is \sqrt[5]{(2^4*3)}^2 ?

The solution to \sqrt[5]{(2^4*3)}^2 is 2*3^{2/5}*2^{3/5}

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simplify \sqrt[5]{(2^4*3)}^2

simplify

2 \cdot 3^{\frac{2}{5}} \cdot 2^{\frac{3}{5}}

Decimal Notation

4.70431 \dots

Solution steps

Apply radical rule:

= (((2^{4} \cdot 3))^{\frac{1}{5}})^{2}

Apply exponent rule:

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

= ((2^{4} \cdot 3))^{\frac{1}{5} \cdot 2}

\frac{1}{5} \cdot 2 = \frac{2}{5}

= ((2^{4} \cdot 3))^{\frac{2}{5}}

Apply exponent rule:

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

= 3^{\frac{2}{5}} (2^{4})^{\frac{2}{5}}

(2^{4})^{\frac{2}{5}} : 2^{\frac{8}{5}}

= 3^{\frac{2}{5}} \cdot 2^{\frac{8}{5}}

2^{\frac{8}{5}} = 2 \cdot 2^{\frac{3}{5}}

= 2 \cdot 3^{\frac{2}{5}} \cdot 2^{\frac{3}{5}}

7.82 \cdot 1 0^{- 3}

e^{- 12.65}

10 e^{6} \cdot e^{5}

e^{x} (6 e^{x})

3.2 x 1 0^{- 2}

What is \sqrt[5]{(2^4*3)}^2 ?
The solution to \sqrt[5]{(2^4*3)}^2 is 2*3^{2/5}*2^{3/5}