Solve frac{12^{6}*54^{-4}*24^{6}*72^{-2}}{6^{4}*27^-3*32^8*36^2*48^-8}

$$\frac { 12 ^ { 6 } \cdot 54 ^ { - 4 } \cdot 24 ^ { 6 } \cdot 72 ^ { - 2 } } { 6 ^ { 4 } \cdot 27 ^ { - 3 } \cdot 32 ^ { 8 } \cdot 36 ^ { 2 } \cdot 48 ^ { - 8 } }$$

Evaluate

$$3888$$

Solution Steps

Calculate 12 to the power of 6 and get 2985984.

$$\frac{2985984\times 54^{-4}\times 24^{6}\times 72^{-2}}{6^{4}\times 27^{-3}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Calculate 54 to the power of -4 and get \frac{1}{8503056}.

$$\frac{2985984\times \frac{1}{8503056}\times 24^{6}\times 72^{-2}}{6^{4}\times 27^{-3}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Multiply 2985984 and \frac{1}{8503056} to get \frac{256}{729}.

$$\frac{\frac{256}{729}\times 24^{6}\times 72^{-2}}{6^{4}\times 27^{-3}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Calculate 24 to the power of 6 and get 191102976.

$$\frac{\frac{256}{729}\times 191102976\times 72^{-2}}{6^{4}\times 27^{-3}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Multiply \frac{256}{729} and 191102976 to get 67108864.

$$\frac{67108864\times 72^{-2}}{6^{4}\times 27^{-3}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Calculate 72 to the power of -2 and get \frac{1}{5184}.

$$\frac{67108864\times \frac{1}{5184}}{6^{4}\times 27^{-3}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Multiply 67108864 and \frac{1}{5184} to get \frac{1048576}{81}.

$$\frac{\frac{1048576}{81}}{6^{4}\times 27^{-3}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Calculate 6 to the power of 4 and get 1296.

$$\frac{\frac{1048576}{81}}{1296\times 27^{-3}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Calculate 27 to the power of -3 and get \frac{1}{19683}.

$$\frac{\frac{1048576}{81}}{1296\times \frac{1}{19683}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Multiply 1296 and \frac{1}{19683} to get \frac{16}{243}.

$$\frac{\frac{1048576}{81}}{\frac{16}{243}\times 32^{8}\times 36^{2}\times 48^{-8}}$$

Calculate 32 to the power of 8 and get 1099511627776.

$$\frac{\frac{1048576}{81}}{\frac{16}{243}\times 1099511627776\times 36^{2}\times 48^{-8}}$$

Multiply \frac{16}{243} and 1099511627776 to get \frac{17592186044416}{243}.

$$\frac{\frac{1048576}{81}}{\frac{17592186044416}{243}\times 36^{2}\times 48^{-8}}$$

Calculate 36 to the power of 2 and get 1296.

$$\frac{\frac{1048576}{81}}{\frac{17592186044416}{243}\times 1296\times 48^{-8}}$$

Multiply \frac{17592186044416}{243} and 1296 to get \frac{281474976710656}{3}.

$$\frac{\frac{1048576}{81}}{\frac{281474976710656}{3}\times 48^{-8}}$$

Calculate 48 to the power of -8 and get \frac{1}{28179280429056}.

$$\frac{\frac{1048576}{81}}{\frac{281474976710656}{3}\times \frac{1}{28179280429056}}$$

Multiply \frac{281474976710656}{3} and \frac{1}{28179280429056} to get \frac{65536}{19683}.

$$\frac{\frac{1048576}{81}}{\frac{65536}{19683}}$$

Divide \frac{1048576}{81} by \frac{65536}{19683} by multiplying \frac{1048576}{81} by the reciprocal of \frac{65536}{19683}.

$$\frac{1048576}{81}\times \frac{19683}{65536}$$

Multiply \frac{1048576}{81} and \frac{19683}{65536} to get 3888.

$$3888$$

Factor

$$2^{4}\times 3^{5}$$