Solve frac{16^frac{1{2}}*9^-1}{sqrt[3]{sqrt{4}4}*sqrt[3]{27}}

$$\frac { 16 ^ { \frac { 1 } { 2 } } \times 9 ^ { - 1 } } { \sqrt[ 3 ] { \sqrt { 4 } 4 } \times \sqrt[ 3 ] { 27 } }$$

Evaluate

$$\frac{2}{27}\approx 0.074074074$$

Solution Steps

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

$$\frac{4\times 9^{-1}}{\sqrt[3]{4\sqrt{4}}\sqrt[3]{27}}$$

Calculate 9 to the power of -1 and get \frac{1}{9}.

$$\frac{4\times \frac{1}{9}}{\sqrt[3]{4\sqrt{4}}\sqrt[3]{27}}$$

Multiply 4 and \frac{1}{9} to get \frac{4}{9}.

$$\frac{\frac{4}{9}}{\sqrt[3]{4\sqrt{4}}\sqrt[3]{27}}$$

Calculate the square root of 4 and get 2.

$$\frac{\frac{4}{9}}{\sqrt[3]{4\times 2}\sqrt[3]{27}}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{4}{9}}{\sqrt[3]{8}\sqrt[3]{27}}$$

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

$$\frac{\frac{4}{9}}{2\sqrt[3]{27}}$$

Calculate \sqrt[3]{27} and get 3.

$$\frac{\frac{4}{9}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{4}{9}}{6}$$

Express \frac{\frac{4}{9}}{6} as a single fraction.

$$\frac{4}{9\times 6}$$

Multiply 9 and 6 to get 54.

$$\frac{4}{54}$$

Reduce the fraction \frac{4}{54} to lowest terms by extracting and canceling out 2.

$$\frac{2}{27}$$

Factor

$$\frac{2}{3 ^ {3}} = 0.07407407407407407$$