Resolver 3^-2(5^-3)/9^7125^-4

$$\frac{ { 3 }^{ -2 } ( { 5 }^{ -3 } ) }{ { 9 }^{ 7 } { 125 }^{ -4 } }$$

Avaliar

$$\frac{1953125}{43046721}\approx 0,045372213$$

Passos Para a Resolução

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

$$\frac{\frac{1}{9}\times 5^{-3}}{9^{7}\times 125^{-4}}$$

Calcule 5 elevado a -3 e obtenha \frac{1}{125}.

$$\frac{\frac{1}{9}\times \frac{1}{125}}{9^{7}\times 125^{-4}}$$

Multiplique \frac{1}{9} e \frac{1}{125} para obter \frac{1}{1125}.

$$\frac{\frac{1}{1125}}{9^{7}\times 125^{-4}}$$

Calcule 9 elevado a 7 e obtenha 4782969.

$$\frac{\frac{1}{1125}}{4782969\times 125^{-4}}$$

Calcule 125 elevado a -4 e obtenha \frac{1}{244140625}.

$$\frac{\frac{1}{1125}}{4782969\times \frac{1}{244140625}}$$

Multiplique 4782969 e \frac{1}{244140625} para obter \frac{4782969}{244140625}.

$$\frac{\frac{1}{1125}}{\frac{4782969}{244140625}}$$

Divida \frac{1}{1125} por \frac{4782969}{244140625} ao multiplicar \frac{1}{1125} pelo recíproco de \frac{4782969}{244140625}.

$$\frac{1}{1125}\times \frac{244140625}{4782969}$$

Multiplique \frac{1}{1125} e \frac{244140625}{4782969} para obter \frac{1953125}{43046721}.

$$\frac{1953125}{43046721}$$

Fatorizar

$$\frac{5 ^ {9}}{3 ^ {16}} = 0,045372213135583546$$