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

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

Calcular

$$\frac{1953125}{43046721}\approx 0.045372213$$

Pasos da solución

Calcula 3 á potencia de -2 e obtén \frac{1}{9}.

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

Calcula 5 á potencia de -3 e obtén \frac{1}{125}.

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

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

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

Calcula 9 á potencia de 7 e obtén 4782969.

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

Calcula 125 á potencia de -4 e obtén \frac{1}{244140625}.

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

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

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

Divide \frac{1}{1125} entre \frac{4782969}{244140625} mediante a multiplicación de \frac{1}{1125} polo recíproco de \frac{4782969}{244140625}.

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

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

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

Factorizar

$$\frac{5 ^ {9}}{3 ^ {16}} = 0.045372213135583546$$