Solve frac{sqrt{3^4}}{sqrt{3^2*5^4}}

$$\frac { \sqrt { 3 ^ { 4 } } } { \sqrt { 3 ^ { 2 } \cdot 5 ^ { 4 } } }$$

Evaluate

$$\frac{3}{25}=0.12$$

Solution Steps

Calculate 3 to the power of 4 and get 81.

$$\frac{\sqrt{81}}{\sqrt{3^{2}\times 5^{4}}}$$

Calculate the square root of 81 and get 9.

$$\frac{9}{\sqrt{3^{2}\times 5^{4}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{\sqrt{9\times 5^{4}}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{9}{\sqrt{9\times 625}}$$

Multiply 9 and 625 to get 5625.

$$\frac{9}{\sqrt{5625}}$$

Calculate the square root of 5625 and get 75.

$$\frac{9}{75}$$

Reduce the fraction \frac{9}{75} to lowest terms by extracting and canceling out 3.

$$\frac{3}{25}$$

Factor

$$\frac{3}{5 ^ {2}} = 0.12$$