Solve (3^{2})^3*(2*3^5)^-2*(18)^2

$$( 3 ^ { 2 } ) ^ { 3 } \times ( 2 \times 3 ^ { 5 } ) ^ { - 2 } \times ( 18 ) ^ { 2 }$$

Evaluate

$$1$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$3^{6}\times \left(2\times 3^{5}\right)^{-2}\times 18^{2}$$

Calculate 3 to the power of 6 and get 729.

$$729\times \left(2\times 3^{5}\right)^{-2}\times 18^{2}$$

Calculate 3 to the power of 5 and get 243.

$$729\times \left(2\times 243\right)^{-2}\times 18^{2}$$

Multiply 2 and 243 to get 486.

$$729\times 486^{-2}\times 18^{2}$$

Calculate 486 to the power of -2 and get \frac{1}{236196}.

$$729\times \frac{1}{236196}\times 18^{2}$$

Multiply 729 and \frac{1}{236196} to get \frac{1}{324}.

$$\frac{1}{324}\times 18^{2}$$

Calculate 18 to the power of 2 and get 324.

$$\frac{1}{324}\times 324$$

Multiply \frac{1}{324} and 324 to get 1.

$$1$$

Factor

$$1$$