Solve frac{sqrt{3^6}:5^2}{sqrt{8^2*2^6}}

$$\frac { \sqrt { 3 ^ { 6 } } : 5 ^ { 2 } } { \sqrt { 8 ^ { 2 } \cdot 2 ^ { 6 } } }$$

Evaluate

$$\frac{27}{1600}=0.016875$$

Solution Steps

Calculate 3 to the power of 6 and get 729.

$$\frac{\frac{\sqrt{729}}{5^{2}}}{\sqrt{8^{2}\times 2^{6}}}$$

Calculate the square root of 729 and get 27.

$$\frac{\frac{27}{5^{2}}}{\sqrt{8^{2}\times 2^{6}}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{27}{25}}{\sqrt{8^{2}\times 2^{6}}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\frac{27}{25}}{\sqrt{64\times 2^{6}}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{\frac{27}{25}}{\sqrt{64\times 64}}$$

Multiply 64 and 64 to get 4096.

$$\frac{\frac{27}{25}}{\sqrt{4096}}$$

Calculate the square root of 4096 and get 64.

$$\frac{\frac{27}{25}}{64}$$

Express \frac{\frac{27}{25}}{64} as a single fraction.

$$\frac{27}{25\times 64}$$

Multiply 25 and 64 to get 1600.

$$\frac{27}{1600}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {6} \cdot 5 ^ {2}} = 0.016875$$