Solve [sqrt{36/25}div(1/2)^4*1/6]^2divsqrt[3]{8}

$$[ \sqrt { \frac { 36 } { 25 } } \div ( \frac { 1 } { 2 } ) ^ { 4 } \times \frac { 1 } { 6 } ] ^ { 2 } \div \sqrt[ 3 ] { 8 }$$

Evaluate

$$\frac{128}{25}=5.12$$

Solution Steps

Rewrite the square root of the division \frac{36}{25} as the division of square roots \frac{\sqrt{36}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{\left(\frac{\frac{6}{5}}{\left(\frac{1}{2}\right)^{4}}\times \frac{1}{6}\right)^{2}}{\sqrt[3]{8}}$$

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{\left(\frac{\frac{6}{5}}{\frac{1}{16}}\times \frac{1}{6}\right)^{2}}{\sqrt[3]{8}}$$

Divide \frac{6}{5} by \frac{1}{16} by multiplying \frac{6}{5} by the reciprocal of \frac{1}{16}.

$$\frac{\left(\frac{6}{5}\times 16\times \frac{1}{6}\right)^{2}}{\sqrt[3]{8}}$$

Multiply \frac{6}{5} and 16 to get \frac{96}{5}.

$$\frac{\left(\frac{96}{5}\times \frac{1}{6}\right)^{2}}{\sqrt[3]{8}}$$

Multiply \frac{96}{5} and \frac{1}{6} to get \frac{16}{5}.

$$\frac{\left(\frac{16}{5}\right)^{2}}{\sqrt[3]{8}}$$

Calculate \frac{16}{5} to the power of 2 and get \frac{256}{25}.

$$\frac{\frac{256}{25}}{\sqrt[3]{8}}$$

Calculate \sqrt[3]{8} and get 2.

$$\frac{\frac{256}{25}}{2}$$

Express \frac{\frac{256}{25}}{2} as a single fraction.

$$\frac{256}{25\times 2}$$

Multiply 25 and 2 to get 50.

$$\frac{256}{50}$$

Reduce the fraction \frac{256}{50} to lowest terms by extracting and canceling out 2.

$$\frac{128}{25}$$

Factor

$$\frac{2 ^ {7}}{5 ^ {2}} = 5\frac{3}{25} = 5.12$$