Solve 9^2frac{9/{left(6frac{6{sqrt{6}}right)}^2}}{}

$$\frac{ { 9 }^{ 2 } \frac{ 9 }{ { \left(6 \frac{ 6 }{ \sqrt{ 6 } } \right) }^{ 2 } } }{ }$$

Evaluate

$$\frac{27}{8}=3.375$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$\frac{81\times \frac{9}{\left(6\times \frac{6}{\sqrt{6}}\right)^{2}}}{1}$$

Rationalize the denominator of \frac{6}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{81\times \frac{9}{\left(6\times \frac{6\sqrt{6}}{\left(\sqrt{6}\right)^{2}}\right)^{2}}}{1}$$

The square of \sqrt{6} is 6.

$$\frac{81\times \frac{9}{\left(6\times \frac{6\sqrt{6}}{6}\right)^{2}}}{1}$$

Cancel out 6 and 6.

$$\frac{81\times \frac{9}{\left(6\sqrt{6}\right)^{2}}}{1}$$

Expand \left(6\sqrt{6}\right)^{2}.

$$\frac{81\times \frac{9}{6^{2}\left(\sqrt{6}\right)^{2}}}{1}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{81\times \frac{9}{36\left(\sqrt{6}\right)^{2}}}{1}$$

The square of \sqrt{6} is 6.

$$\frac{81\times \frac{9}{36\times 6}}{1}$$

Multiply 36 and 6 to get 216.

$$\frac{81\times \frac{9}{216}}{1}$$

Reduce the fraction \frac{9}{216} to lowest terms by extracting and canceling out 9.

$$\frac{81\times \frac{1}{24}}{1}$$

Multiply 81 and \frac{1}{24} to get \frac{27}{8}.

$$\frac{\frac{27}{8}}{1}$$

Anything divided by one gives itself.

$$\frac{27}{8}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {3}} = 3\frac{3}{8} = 3.375$$