What is \sqrt[6]{2^4}*\sqrt[5]{2^3} ?

The solution to \sqrt[6]{2^4}*\sqrt[5]{2^3} is 2*2^{4/15}

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simplify \sqrt[6]{2^4}*\sqrt[5]{2^3}

simplify

6 2^{4} \cdot 5 2^{3}

2 \cdot 2^{\frac{4}{15}}

Decimal

2.40605 \dots

Solution steps

6 2^{4} 5 2^{3}

6 2^{4} : 2^{\frac{2}{3}}

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

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

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

Apply exponent rule:

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

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

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

Join

\frac{2}{3} + \frac{3}{5} : \frac{19}{15}

= 2^{\frac{19}{15}}

2^{\frac{19}{15}} = 2^{1 + \frac{4}{15}}

= 2^{1 + \frac{4}{15}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 2^{1} \cdot 2^{\frac{4}{15}}

Refine

= 2 \cdot 2^{\frac{4}{15}}

7 x e^{- x}

(6 3^{5})^{4}

\frac{x + 3}{2 - x}

e^{- \frac{4}{n}}

e^{- 3 t} cos (4 t)

What is \sqrt[6]{2^4}*\sqrt[5]{2^3} ?
The solution to \sqrt[6]{2^4}*\sqrt[5]{2^3} is 2*2^{4/15}