What is \sqrt[ 3/2 ]{8^2}\sqrt[ 5/3 ]{32^2} ?

The solution to \sqrt[ 3/2 ]{8^2}\sqrt[ 5/3 ]{32^2} is 1024

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simplify \sqrt[ 3/2 ]{8^2}\sqrt[ 5/3 ]{32^2}

simplify

1024

Solution steps

= 8^{\frac{4}{3}} \cdot 3 2^{\frac{6}{5}}

Factor integer

8 = 2^{3}

= (2^{3})^{\frac{4}{3}} \cdot 3 2^{\frac{6}{5}}

Apply exponent rule:

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

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

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

Refine

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

Factor integer

32 = 2^{5}

= 2^{4} (2^{5})^{\frac{6}{5}}

Apply exponent rule:

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

(2^{5})^{\frac{6}{5}} = 2^{5 \cdot \frac{6}{5}}

= 2^{4} \cdot 2^{5 \cdot \frac{6}{5}}

Refine

= 2^{4} \cdot 2^{6}

Apply exponent rule:

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

2^{4} \cdot 2^{6} = 2^{4 + 6}

= 2^{4 + 6}

Add the numbers:

4 + 6 = 10

= 2^{10}

2^{10} = 1024

= 1024

\frac{1 + 4 x ^{2}}{1 - x ^{2}}

0.011 \cdot 1 0^{- 6}

3.225 \cdot 1 0^{- 5}

(1 \cdot 1 0^{8}) (e^{- 0.157 (7)})

2 e^{- \frac{1}{2}} \cdot 2 x

What is \sqrt[ 3/2 ]{8^2}\sqrt[ 5/3 ]{32^2} ?
The solution to \sqrt[ 3/2 ]{8^2}\sqrt[ 5/3 ]{32^2} is 1024