What is (64*sqrt(2)*(1/4)^2)/(2^{3/2)} ?

The solution to (64*sqrt(2)*(1/4)^2)/(2^{3/2)} is 2

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simplify (64sqrt(2)(1/4)^2)/(2^{3/2)}

simplify

\frac{64 \cdot 2 \cdot ( \frac{1}{4} ) ^{2}}{2 ^{\frac{3}{2}}}

2

Solution steps

\frac{64 2 ( \frac{1}{4} ) ^{2}}{2 ^{\frac{3}{2}}}

Factor the number:

64 = 2^{6}

= \frac{2 ^{6} 2 ( \frac{1}{4} ) ^{2}}{2 ^{\frac{3}{2}}}

Simplify

\frac{2 ^{6}}{2 ^{\frac{3}{2}}} : 2^{\frac{9}{2}}

= 2^{\frac{9}{2}} 2 (\frac{1}{4})^{2}

2^{\frac{9}{2}} 2 (\frac{1}{4})^{2} = 2

= 2

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What is (64*sqrt(2)*(1/4)^2)/(2^{3/2)} ?
The solution to (64*sqrt(2)*(1/4)^2)/(2^{3/2)} is 2