Solve (30^-3625^3/72^2243^-2)

$$( \frac { 30 ^ { - 3 } 625 ^ { 3 } } { 72 ^ { 2 } 243 ^ { - 2 } } )$$

Evaluate

$$\frac{52734375}{512}=102996.826171875$$

Solution Steps

Calculate 30 to the power of -3 and get \frac{1}{27000}.

$$\frac{\frac{1}{27000}\times 625^{3}}{72^{2}\times 243^{-2}}$$

Calculate 625 to the power of 3 and get 244140625.

$$\frac{\frac{1}{27000}\times 244140625}{72^{2}\times 243^{-2}}$$

Multiply \frac{1}{27000} and 244140625 to get \frac{1953125}{216}.

$$\frac{\frac{1953125}{216}}{72^{2}\times 243^{-2}}$$

Calculate 72 to the power of 2 and get 5184.

$$\frac{\frac{1953125}{216}}{5184\times 243^{-2}}$$

Calculate 243 to the power of -2 and get \frac{1}{59049}.

$$\frac{\frac{1953125}{216}}{5184\times \frac{1}{59049}}$$

Multiply 5184 and \frac{1}{59049} to get \frac{64}{729}.

$$\frac{\frac{1953125}{216}}{\frac{64}{729}}$$

Divide \frac{1953125}{216} by \frac{64}{729} by multiplying \frac{1953125}{216} by the reciprocal of \frac{64}{729}.

$$\frac{1953125}{216}\times \frac{729}{64}$$

Multiply \frac{1953125}{216} and \frac{729}{64} to get \frac{52734375}{512}.

$$\frac{52734375}{512}$$

Factor

$$\frac{3 ^ {3} \cdot 5 ^ {9}}{2 ^ {9}} = 102996\frac{423}{512} = 102996.826171875$$