Solve (3/4)^2*sqrt{(frac{1/8)^2}}{sqrt[4]{(3/4)^4}}

$$\frac { ( \frac { 3 } { 4 } ) ^ { 2 } \cdot \sqrt { ( \frac { 1 } { 8 } ) ^ { 2 } } } { \sqrt[ 4 ] { ( \frac { 3 } { 4 } ) ^ { 4 } } }$$

Evaluate

$$\frac{3}{32}=0.09375$$

Solution Steps

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{\frac{9}{16}\sqrt{\left(\frac{1}{8}\right)^{2}}}{\sqrt[4]{\left(\frac{3}{4}\right)^{4}}}$$

Calculate \frac{1}{8} to the power of 2 and get \frac{1}{64}.

$$\frac{\frac{9}{16}\sqrt{\frac{1}{64}}}{\sqrt[4]{\left(\frac{3}{4}\right)^{4}}}$$

Rewrite the square root of the division \frac{1}{64} as the division of square roots \frac{\sqrt{1}}{\sqrt{64}}. Take the square root of both numerator and denominator.

$$\frac{\frac{9}{16}\times \frac{1}{8}}{\sqrt[4]{\left(\frac{3}{4}\right)^{4}}}$$

Multiply \frac{9}{16} and \frac{1}{8} to get \frac{9}{128}.

$$\frac{\frac{9}{128}}{\sqrt[4]{\left(\frac{3}{4}\right)^{4}}}$$

Calculate \frac{3}{4} to the power of 4 and get \frac{81}{256}.

$$\frac{\frac{9}{128}}{\sqrt[4]{\frac{81}{256}}}$$

Calculate \sqrt[4]{\frac{81}{256}} and get \frac{3}{4}.

$$\frac{\frac{9}{128}}{\frac{3}{4}}$$

Divide \frac{9}{128} by \frac{3}{4} by multiplying \frac{9}{128} by the reciprocal of \frac{3}{4}.

$$\frac{9}{128}\times \frac{4}{3}$$

Multiply \frac{9}{128} and \frac{4}{3} to get \frac{3}{32}.

$$\frac{3}{32}$$

Factor

$$\frac{3}{2 ^ {5}} = 0.09375$$