Resolver ((-1/4)^{3}:(-1/4)+(2-1/2)^{4}(1-5/9)^2):[(frac{17}{2})^4:(frac{17}{2})^3+frac{3}{2}*(-1)^2-1+frac{1}{4}]*frac{37}{2}

$$( ( - \frac { 1 } { 4 } ) ^ { 3 } : ( - \frac { 1 } { 4 } ) + ( 2 - \frac { 1 } { 2 } ) ^ { 4 } ( 1 - \frac { 5 } { 9 } ) ^ { 2 } ) : [ ( \frac { 17 } { 2 } ) ^ { 4 } : ( \frac { 17 } { 2 } ) ^ { 3 } + \frac { 3 } { 2 } \cdot ( - 1 ) ^ { 2 } - 1 + \frac { 1 } { 4 } ] \cdot \frac { 37 } { 2 }$$

Avaliar

$$\frac{17}{8}=2,125$$

Passos Para a Resolução

Para dividir as potências da mesma base, subtraia o expoente do denominador do expoente do numerador. Subtraia 1 de 3 para obter 2.

$$\frac{\left(-\frac{1}{4}\right)^{2}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\frac{\left(\frac{17}{2}\right)^{4}}{\left(\frac{17}{2}\right)^{3}}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Para dividir as potências da mesma base, subtraia o expoente do denominador do expoente do numerador. Subtraia 3 de 4 para obter 1.

$$\frac{\left(-\frac{1}{4}\right)^{2}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Calcule -\frac{1}{4} elevado a 2 e obtenha \frac{1}{16}.

$$\frac{\frac{1}{16}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Subtraia \frac{1}{2} de 2 para obter \frac{3}{2}.

$$\frac{\frac{1}{16}+\left(\frac{3}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

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

$$\frac{\frac{1}{16}+\frac{81}{16}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Subtraia \frac{5}{9} de 1 para obter \frac{4}{9}.

$$\frac{\frac{1}{16}+\frac{81}{16}\times \left(\frac{4}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Calcule \frac{4}{9} elevado a 2 e obtenha \frac{16}{81}.

$$\frac{\frac{1}{16}+\frac{81}{16}\times \frac{16}{81}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Multiplique \frac{81}{16} e \frac{16}{81} para obter 1.

$$\frac{\frac{1}{16}+1}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Some \frac{1}{16} e 1 para obter \frac{17}{16}.

$$\frac{\frac{17}{16}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Calcule \frac{17}{2} elevado a 1 e obtenha \frac{17}{2}.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Calcule -1 elevado a 2 e obtenha 1.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}\times 1-1+\frac{1}{4}}\times \frac{37}{2}$$

Multiplique \frac{3}{2} e 1 para obter \frac{3}{2}.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Some \frac{17}{2} e \frac{3}{2} para obter 10.

$$\frac{\frac{17}{16}}{10-1+\frac{1}{4}}\times \frac{37}{2}$$

Subtraia 1 de 10 para obter 9.

$$\frac{\frac{17}{16}}{9+\frac{1}{4}}\times \frac{37}{2}$$

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

$$\frac{\frac{17}{16}}{\frac{37}{4}}\times \frac{37}{2}$$

Divida \frac{17}{16} por \frac{37}{4} ao multiplicar \frac{17}{16} pelo recíproco de \frac{37}{4}.

$$\frac{17}{16}\times \frac{4}{37}\times \frac{37}{2}$$

Multiplique \frac{17}{16} e \frac{4}{37} para obter \frac{17}{148}.

$$\frac{17}{148}\times \frac{37}{2}$$

Multiplique \frac{17}{148} e \frac{37}{2} para obter \frac{17}{8}.

$$\frac{17}{8}$$

Fatorizar

$$\frac{17}{2 ^ {3}} = 2\frac{1}{8} = 2,125$$