Solve frac{8^{2}*9^{2}*3^3}{16^2*3^6*5^2}

$$\frac { 8 ^ { 2 } \times 9 ^ { 2 } \times 3 ^ { 3 } } { 16 ^ { 2 } \times 3 ^ { 6 } \times 5 ^ { 2 } }$$

Evaluate

$$\frac{3}{100}=0.03$$

Solution Steps

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

$$\frac{8^{2}\times 9^{2}}{3^{3}\times 5^{2}\times 16^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{64\times 9^{2}}{3^{3}\times 5^{2}\times 16^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{64\times 81}{3^{3}\times 5^{2}\times 16^{2}}$$

Multiply 64 and 81 to get 5184.

$$\frac{5184}{3^{3}\times 5^{2}\times 16^{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{5184}{27\times 5^{2}\times 16^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{5184}{27\times 25\times 16^{2}}$$

Multiply 27 and 25 to get 675.

$$\frac{5184}{675\times 16^{2}}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{5184}{675\times 256}$$

Multiply 675 and 256 to get 172800.

$$\frac{5184}{172800}$$

Reduce the fraction \frac{5184}{172800} to lowest terms by extracting and canceling out 1728.

$$\frac{3}{100}$$

Factor

$$\frac{3}{2 ^ {2} \cdot 5 ^ {2}} = 0.03$$