Solve ((frac{2/3)^{4}(3/2)^2}{2^2+(1/3)^2})^2=

$$( \frac { ( \frac { 2 } { 3 } ) ^ { 4 } ( \frac { 3 } { 2 } ) ^ { 2 } } { 2 ^ { 2 } + ( \frac { 1 } { 3 } ) ^ { 2 } } ) ^ { 2 } =$$

Evaluate

$$\frac{16}{1369}\approx 0.011687363$$

Solution Steps

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\left(\frac{\frac{16}{81}\times \left(\frac{3}{2}\right)^{2}}{2^{2}+\left(\frac{1}{3}\right)^{2}}\right)^{2}$$

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

$$\left(\frac{\frac{16}{81}\times \frac{9}{4}}{2^{2}+\left(\frac{1}{3}\right)^{2}}\right)^{2}$$

Multiply \frac{16}{81} and \frac{9}{4} to get \frac{4}{9}.

$$\left(\frac{\frac{4}{9}}{2^{2}+\left(\frac{1}{3}\right)^{2}}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{\frac{4}{9}}{4+\left(\frac{1}{3}\right)^{2}}\right)^{2}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\left(\frac{\frac{4}{9}}{4+\frac{1}{9}}\right)^{2}$$

Add 4 and \frac{1}{9} to get \frac{37}{9}.

$$\left(\frac{\frac{4}{9}}{\frac{37}{9}}\right)^{2}$$

Divide \frac{4}{9} by \frac{37}{9} by multiplying \frac{4}{9} by the reciprocal of \frac{37}{9}.

$$\left(\frac{4}{9}\times \frac{9}{37}\right)^{2}$$

Multiply \frac{4}{9} and \frac{9}{37} to get \frac{4}{37}.

$$\left(\frac{4}{37}\right)^{2}$$

Calculate \frac{4}{37} to the power of 2 and get \frac{16}{1369}.

$$\frac{16}{1369}$$

Factor

$$\frac{2 ^ {4}}{37 ^ {2}} = 0.01168736303871439$$