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

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

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

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

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

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

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

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.

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

Multiply \frac{9}{16} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{9\times 1}{16\times 8}.

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

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

$$\frac{\frac{9}{128}}{\sqrt{\frac{81}{256}}}$$

Rewrite the square root of the division \frac{81}{256} as the division of square roots \frac{\sqrt{81}}{\sqrt{256}}. Take the square root of both numerator and denominator.

$$\frac{\frac{9}{128}}{\frac{9}{16}}$$

Divide \frac{9}{128} by \frac{9}{16} by multiplying \frac{9}{128} by the reciprocal of \frac{9}{16}.

$$\frac{9}{128}\times \frac{16}{9}$$

Multiply \frac{9}{128} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 16}{128\times 9}$$

Cancel out 9 in both numerator and denominator.

$$\frac{16}{128}$$

Reduce the fraction \frac{16}{128} to lowest terms by extracting and canceling out 16.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$