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

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

Evaluate

$$\frac{16}{361}\approx 0.04432133$$

Solution Steps

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

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

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

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

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

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

Calculate 2 to the power of 1 and get 2.

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

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

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

Add 2 and \frac{1}{9} to get \frac{19}{9}.

$$\left(\frac{\frac{4}{9}}{\frac{19}{9}}\right)^{2}$$

Divide \frac{4}{9} by \frac{19}{9} by multiplying \frac{4}{9} by the reciprocal of \frac{19}{9}.

$$\left(\frac{4}{9}\times \frac{9}{19}\right)^{2}$$

Multiply \frac{4}{9} and \frac{9}{19} to get \frac{4}{19}.

$$\left(\frac{4}{19}\right)^{2}$$

Calculate \frac{4}{19} to the power of 2 and get \frac{16}{361}.

$$\frac{16}{361}$$

Factor

$$\frac{2 ^ {4}}{19 ^ {2}} = 0.0443213296398892$$