What is \sqrt[3]{2^2}*\sqrt[8]{2^7}*sqrt(2) ?

The solution to \sqrt[3]{2^2}*\sqrt[8]{2^7}*sqrt(2) is 2*2^{13/24}sqrt(2)

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simplify \sqrt[3]{2^2}\sqrt[8]{2^7}sqrt(2)

simplify

2 \cdot 2^{\frac{13}{24}} 2

Decimal Notation

4.11720 \dots

Solution steps

= 2^{\frac{2}{3}} \cdot 2^{\frac{7}{8}} 2

Apply exponent rule:

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

2^{\frac{2}{3}} \cdot 2^{\frac{7}{8}} = 2^{\frac{2}{3} + \frac{7}{8}}

= 2^{\frac{2}{3} + \frac{7}{8}} 2

2^{\frac{2}{3} + \frac{7}{8}} = 2 \cdot 2^{\frac{13}{24}}

= 2 \cdot 2^{\frac{13}{24}} 2

5.1 \cdot 1 0^{- 10}

2.5 \cdot 60 0^{0.75} \cdot 10 0^{- 0.75}

(1.2 \cdot 1 0^{- 5} (c)^{- 1}) \cdot 5 c

What is \sqrt[3]{2^2}*\sqrt[8]{2^7}*sqrt(2) ?
The solution to \sqrt[3]{2^2}*\sqrt[8]{2^7}*sqrt(2) is 2*2^{13/24}sqrt(2)