Solve sqrt{3^6:(6-3)^4/5^4*3^8}

$$\sqrt { \frac { 3 ^ { 6 } : ( 6 - 3 ) ^ { 4 } } { 5 ^ { 4 } \times 3 ^ { 8 } } }$$

Evaluate

$$\frac{1}{675}\approx 0.001481481$$

Solution Steps

Calculate 3 to the power of 6 and get 729.

$$\sqrt{\frac{\frac{729}{\left(6-3\right)^{4}}}{5^{4}\times 3^{8}}}$$

Subtract 3 from 6 to get 3.

$$\sqrt{\frac{\frac{729}{3^{4}}}{5^{4}\times 3^{8}}}$$

Calculate 3 to the power of 4 and get 81.

$$\sqrt{\frac{\frac{729}{81}}{5^{4}\times 3^{8}}}$$

Divide 729 by 81 to get 9.

$$\sqrt{\frac{9}{5^{4}\times 3^{8}}}$$

Calculate 5 to the power of 4 and get 625.

$$\sqrt{\frac{9}{625\times 3^{8}}}$$

Calculate 3 to the power of 8 and get 6561.

$$\sqrt{\frac{9}{625\times 6561}}$$

Multiply 625 and 6561 to get 4100625.

$$\sqrt{\frac{9}{4100625}}$$

Reduce the fraction \frac{9}{4100625} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{1}{455625}}$$

Rewrite the square root of the division \frac{1}{455625} as the division of square roots \frac{\sqrt{1}}{\sqrt{455625}}. Take the square root of both numerator and denominator.

$$\frac{1}{675}$$

Factor

$$\frac{1}{3 ^ {3} \cdot 5 ^ {2}} = 0.0014814814814814814$$