Evaluate (11^7* square root of 6)/(11^5*6^(3/2))

$\frac{11^{7} \cdot \sqrt{6}}{11^{5} \cdot 6^{\frac{3}{2}}}$

Factor $11^{5}$ out of $11^{7} \cdot \sqrt{6}$ .

$\frac{11^{5} (11^{2} \cdot \sqrt{6})}{11^{5} \cdot 6^{\frac{3}{2}}}$

Cancel the common factors.

Factor $11^{5}$ out of $11^{5} \cdot 6^{\frac{3}{2}}$ .

$\frac{11^{5} (11^{2} \cdot \sqrt{6})}{11^{5} (6^{\frac{3}{2}})}$

Cancel the common factor.

$\frac{11^{5} (11^{2} \cdot \sqrt{6})}{11^{5} \cdot 6^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{11^{2} \cdot \sqrt{6}}{6^{\frac{3}{2}}}$

Raise $11$ to the power of $2$ .

$\frac{121 \sqrt{6}}{6^{\frac{3}{2}}}$

The result can be shown in multiple forms.

Exact Form:

$\frac{121 \sqrt{6}}{6^{\frac{3}{2}}}$

Decimal Form:

$20.1\overline{6}$