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

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

Avaliar

$$\frac{16}{361}\approx 0,04432133$$

Passos Para a Resolução

Calcule \frac{2}{3} elevado a 4 e obtenha \frac{16}{81}.

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

Calcule \frac{3}{2} elevado a 2 e obtenha \frac{9}{4}.

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

Multiplique \frac{16}{81} e \frac{9}{4} para obter \frac{4}{9}.

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

Calcule 2 elevado a 1 e obtenha 2.

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

Calcule \frac{1}{3} elevado a 2 e obtenha \frac{1}{9}.

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

Some 2 e \frac{1}{9} para obter \frac{19}{9}.

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

Divida \frac{4}{9} por \frac{19}{9} ao multiplicar \frac{4}{9} pelo recíproco de \frac{19}{9}.

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

Multiplique \frac{4}{9} e \frac{9}{19} para obter \frac{4}{19}.

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

Calcule \frac{4}{19} elevado a 2 e obtenha \frac{16}{361}.

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

Fatorizar

$$\frac{2 ^ {4}}{19 ^ {2}} = 0,0443213296398892$$