Solve sqrt{(frac{1/81)^2}}{sqrt{9/16}}

$$\frac { \sqrt { ( \frac { 1 } { 81 } ) ^ { 2 } } } { \sqrt { \frac { 9 } { 16 } } }$$

Evaluate

$$\frac{4}{243}\approx 0.016460905$$

Solution Steps

Calculate \frac{1}{81} to the power of 2 and get \frac{1}{6561}.

$$\frac{\sqrt{\frac{1}{6561}}}{\sqrt{\frac{9}{16}}}$$

Rewrite the square root of the division \frac{1}{6561} as the division of square roots \frac{\sqrt{1}}{\sqrt{6561}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{81}}{\sqrt{\frac{9}{16}}}$$

Rewrite the square root of the division \frac{9}{16} as the division of square roots \frac{\sqrt{9}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{81}}{\frac{3}{4}}$$

Divide \frac{1}{81} by \frac{3}{4} by multiplying \frac{1}{81} by the reciprocal of \frac{3}{4}.

$$\frac{1}{81}\times \frac{4}{3}$$

Multiply \frac{1}{81} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{81\times 3}$$

Do the multiplications in the fraction \frac{1\times 4}{81\times 3}.

$$\frac{4}{243}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {5}} = 0.01646090534979424$$