Solve frac{(27^{3})(8^3)(2^4)}{(3^4)(4)(9)^10}

$$\frac { ( 27 ^ { 3 } ) ( 8 ^ { 3 } ) ( 2 ^ { 4 } ) } { ( 3 ^ { 4 } ) ( 4 ) ( 9 ) ^ { 10 } }$$

Evaluate

$$\frac{2048}{14348907}\approx 0.000142729$$

Solution Steps

Calculate 27 to the power of 3 and get 19683.

$$\frac{19683\times 8^{3}\times 2^{4}}{3^{4}\times 4\times 9^{10}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{19683\times 512\times 2^{4}}{3^{4}\times 4\times 9^{10}}$$

Multiply 19683 and 512 to get 10077696.

$$\frac{10077696\times 2^{4}}{3^{4}\times 4\times 9^{10}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{10077696\times 16}{3^{4}\times 4\times 9^{10}}$$

Multiply 10077696 and 16 to get 161243136.

$$\frac{161243136}{3^{4}\times 4\times 9^{10}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{161243136}{81\times 4\times 9^{10}}$$

Multiply 81 and 4 to get 324.

$$\frac{161243136}{324\times 9^{10}}$$

Calculate 9 to the power of 10 and get 3486784401.

$$\frac{161243136}{324\times 3486784401}$$

Multiply 324 and 3486784401 to get 1129718145924.

$$\frac{161243136}{1129718145924}$$

Reduce the fraction \frac{161243136}{1129718145924} to lowest terms by extracting and canceling out 78732.

$$\frac{2048}{14348907}$$

Factor

$$\frac{2 ^ {11}}{3 ^ {15}} = 0.00014272864128257295$$