Solve frac{(3^{2})^3*(2^4)^2}{9*3^6*64}

$$\frac { ( 3 ^ { 2 } ) ^ { 3 } \cdot ( 2 ^ { 4 } ) ^ { 2 } } { 9 \cdot 3 ^ { 6 } \cdot 64 }$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

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

$$\frac{3^{6}\times \left(2^{4}\right)^{2}}{9\times 3^{6}\times 64}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{3^{6}\times 2^{8}}{9\times 3^{6}\times 64}$$

Cancel out 3^{6} in both numerator and denominator.

$$\frac{2^{8}}{9\times 64}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{256}{9\times 64}$$

Multiply 9 and 64 to get 576.

$$\frac{256}{576}$$

Reduce the fraction \frac{256}{576} to lowest terms by extracting and canceling out 64.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$