What is \sqrt[3]{2^2}*\sqrt[9]{2^7}*sqrt(2) ?

The solution to \sqrt[3]{2^2}*\sqrt[9]{2^7}*sqrt(2) is 2*2^{4/9}sqrt(2)

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simplify \sqrt[3]{2^2}\sqrt[9]{2^7}sqrt(2)

simplify

3 2^{2} \cdot 9 2^{7} \cdot 2

2 \cdot 2^{\frac{4}{9}} 2

Decimal

3.84889 \dots

Solution steps

3 2^{2} 9 2^{7} 2

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

= 2^{\frac{2}{3}} 9 2^{7} 2

9 2^{7} : 2^{\frac{7}{9}}

= 2^{\frac{2}{3}} \cdot 2^{\frac{7}{9}} 2

Apply exponent rule:

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

2^{\frac{2}{3}} \cdot 2^{\frac{7}{9}} = 2^{\frac{2}{3} + \frac{7}{9}}

= 2^{\frac{2}{3} + \frac{7}{9}} 2

2^{\frac{2}{3} + \frac{7}{9}} = 2 \cdot 2^{\frac{4}{9}}

= 2 \cdot 2^{\frac{4}{9}} 2

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What is \sqrt[3]{2^2}*\sqrt[9]{2^7}*sqrt(2) ?
The solution to \sqrt[3]{2^2}*\sqrt[9]{2^7}*sqrt(2) is 2*2^{4/9}sqrt(2)