Solve (2*9)^12div[(9*2)^5*2^7]*9^3

$$( 2 \cdot 9 ) ^ { 12 } \div [ ( 9 \cdot 2 ) ^ { 5 } \cdot 2 ^ { 7 } ] \cdot 9 ^ { 3 }$$

Evaluate

$$3486784401$$

Solution Steps

Cancel out \left(2\times 9\right)^{5} in both numerator and denominator.

$$\frac{\left(2\times 9\right)^{7}}{2^{7}}\times 9^{3}$$

Multiply 2 and 9 to get 18.

$$\frac{18^{7}}{2^{7}}\times 9^{3}$$

Calculate 18 to the power of 7 and get 612220032.

$$\frac{612220032}{2^{7}}\times 9^{3}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{612220032}{128}\times 9^{3}$$

Divide 612220032 by 128 to get 4782969.

$$4782969\times 9^{3}$$

Calculate 9 to the power of 3 and get 729.

$$4782969\times 729$$

Multiply 4782969 and 729 to get 3486784401.

$$3486784401$$

Factor

$$3^{20}$$