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

The solution to \sqrt[3]{2^2}*\sqrt[4]{2^3} is 2*2^{5/12}

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

simplify

2 \cdot 2^{\frac{5}{12}}

Decimal Notation

2.66967 \dots

Solution steps

= 2^{\frac{2}{3}} \cdot 2^{\frac{3}{4}}

Apply exponent rule:

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

2^{\frac{2}{3}} \cdot 2^{\frac{3}{4}} = 2^{\frac{2}{3} + \frac{3}{4}}

= 2^{\frac{2}{3} + \frac{3}{4}}

Join

\frac{2}{3} + \frac{3}{4} : \frac{17}{12}

= 2^{\frac{17}{12}}

2^{\frac{17}{12}} = 2^{1 + \frac{5}{12}}

= 2^{1 + \frac{5}{12}}

Apply exponent rule:

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

= 2^{1} \cdot 2^{\frac{5}{12}}

Refine

= 2 \cdot 2^{\frac{5}{12}}

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What is \sqrt[3]{2^2}*\sqrt[4]{2^3} ?
The solution to \sqrt[3]{2^2}*\sqrt[4]{2^3} is 2*2^{5/12}