Solve sqrt{3^8/(4+2)^4}=

$$\sqrt { \frac { 3 ^ { 8 } } { ( 4 + 2 ) ^ { 4 } } } =$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Calculate 3 to the power of 8 and get 6561.

$$\sqrt{\frac{6561}{\left(4+2\right)^{4}}}$$

Add 4 and 2 to get 6.

$$\sqrt{\frac{6561}{6^{4}}}$$

Calculate 6 to the power of 4 and get 1296.

$$\sqrt{\frac{6561}{1296}}$$

Reduce the fraction \frac{6561}{1296} to lowest terms by extracting and canceling out 81.

$$\sqrt{\frac{81}{16}}$$

Rewrite the square root of the division \frac{81}{16} as the division of square roots \frac{\sqrt{81}}{\sqrt{16}}. Take the square root of both numerator and denominator.

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

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$