Solve (3^{2})^{3}(2*6^5)^-2(2^2)^3

$$( 3 ^ { 2 } ) ^ { 3 } ( 2 \cdot 6 ^ { 5 } ) ^ { - 2 } ( 2 ^ { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{1}{5184}\approx 0.000192901$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 6 and get 729.

$$729\times \left(2\times 6^{5}\right)^{-2}\times 2^{6}$$

Calculate 6 to the power of 5 and get 7776.

$$729\times \left(2\times 7776\right)^{-2}\times 2^{6}$$

Multiply 2 and 7776 to get 15552.

$$729\times 15552^{-2}\times 2^{6}$$

Calculate 15552 to the power of -2 and get \frac{1}{241864704}.

$$729\times \frac{1}{241864704}\times 2^{6}$$

Multiply 729 and \frac{1}{241864704} to get \frac{1}{331776}.

$$\frac{1}{331776}\times 2^{6}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{1}{331776}\times 64$$

Multiply \frac{1}{331776} and 64 to get \frac{1}{5184}.

$$\frac{1}{5184}$$

Factor

$$\frac{1}{2 ^ {6} \cdot 3 ^ {4}} = 0.00019290123456790122$$