Solve 18:sqrt{3^3*sqrt{3^3:sqrt{3^2}}}

$$18 : \sqrt { 3 ^ { 3 } \cdot \sqrt { 3 ^ { 3 } : \sqrt { 3 ^ { 2 } } } }$$

Evaluate

$$2$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{18}{\sqrt{27\sqrt{\frac{3^{3}}{\sqrt{3^{2}}}}}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{18}{\sqrt{27\sqrt{\frac{27}{\sqrt{3^{2}}}}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{18}{\sqrt{27\sqrt{\frac{27}{\sqrt{9}}}}}$$

Calculate the square root of 9 and get 3.

$$\frac{18}{\sqrt{27\sqrt{\frac{27}{3}}}}$$

Divide 27 by 3 to get 9.

$$\frac{18}{\sqrt{27\sqrt{9}}}$$

Calculate the square root of 9 and get 3.

$$\frac{18}{\sqrt{27\times 3}}$$

Multiply 27 and 3 to get 81.

$$\frac{18}{\sqrt{81}}$$

Calculate the square root of 81 and get 9.

$$\frac{18}{9}$$

Divide 18 by 9 to get 2.

$$2$$

Factor

$$2$$