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

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

Avaliar

$$\frac{16}{1369}\approx 0,011687363$$

Passos Para a Resolução

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

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

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

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

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

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

Calcule 2 elevado a 2 e obtenha 4.

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

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

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

Some 4 e \frac{1}{9} para obter \frac{37}{9}.

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

Divida \frac{4}{9} por \frac{37}{9} ao multiplicar \frac{4}{9} pelo recíproco de \frac{37}{9}.

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

Multiplique \frac{4}{9} e \frac{9}{37} para obter \frac{4}{37}.

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

Calcule \frac{4}{37} elevado a 2 e obtenha \frac{16}{1369}.

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

Fatorizar

$$\frac{2 ^ {4}}{37 ^ {2}} = 0,01168736303871439$$