Resolver ((frac{1/2)^{2}3^{-1}25^3}{(1/5)^-54^-29})^-1

$$( \frac { ( \frac { 1 } { 2 } ) ^ { 2 } 3 ^ { - 1 } 25 ^ { 3 } } { ( \frac { 1 } { 5 } ) ^ { - 5 } 4 ^ { - 2 } 9 } ) ^ { - 1 }$$

Avaliar

$$\frac{27}{20}=1,35$$

Passos Para a Resolução

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

$$\left(\frac{\frac{1}{4}\times 3^{-1}\times 25^{3}}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

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

$$\left(\frac{\frac{1}{4}\times \frac{1}{3}\times 25^{3}}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

Multiplique \frac{1}{4} e \frac{1}{3} para obter \frac{1}{12}.

$$\left(\frac{\frac{1}{12}\times 25^{3}}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

Calcule 25 elevado a 3 e obtenha 15625.

$$\left(\frac{\frac{1}{12}\times 15625}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

Multiplique \frac{1}{12} e 15625 para obter \frac{15625}{12}.

$$\left(\frac{\frac{15625}{12}}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

Calcule \frac{1}{5} elevado a -5 e obtenha 3125.

$$\left(\frac{\frac{15625}{12}}{3125\times 4^{-2}\times 9}\right)^{-1}$$

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

$$\left(\frac{\frac{15625}{12}}{3125\times \frac{1}{16}\times 9}\right)^{-1}$$

Multiplique 3125 e \frac{1}{16} para obter \frac{3125}{16}.

$$\left(\frac{\frac{15625}{12}}{\frac{3125}{16}\times 9}\right)^{-1}$$

Multiplique \frac{3125}{16} e 9 para obter \frac{28125}{16}.

$$\left(\frac{\frac{15625}{12}}{\frac{28125}{16}}\right)^{-1}$$

Divida \frac{15625}{12} por \frac{28125}{16} ao multiplicar \frac{15625}{12} pelo recíproco de \frac{28125}{16}.

$$\left(\frac{15625}{12}\times \frac{16}{28125}\right)^{-1}$$

Multiplique \frac{15625}{12} e \frac{16}{28125} para obter \frac{20}{27}.

$$\left(\frac{20}{27}\right)^{-1}$$

Calcule \frac{20}{27} elevado a -1 e obtenha \frac{27}{20}.

$$\frac{27}{20}$$

Fatorizar

$$\frac{3 ^ {3}}{2 ^ {2} \cdot 5} = 1\frac{7}{20} = 1,35$$