Solve for: (6^{-2} * 216)/(sqrt(6))

Expression: $\frac{ {6}^{-2} \times 216 }{ \sqrt{ 6 } }$

Write the number in exponential form with the base of $6$

$\frac{ {6}^{-2} \times {6}^{3} }{ \sqrt{ 6 } }$

Calculate the product

$\frac{ 6 }{ \sqrt{ 6 } }$

Multiply the fraction by $\frac{ \sqrt{ 6 } }{ \sqrt{ 6 } }$

$\frac{ 6 }{ \sqrt{ 6 } } \times \frac{ \sqrt{ 6 } }{ \sqrt{ 6 } }$

To multiply the fractions, multiply the numerators and denominators separately

$\frac{ 6\sqrt{ 6 } }{ \sqrt{ 6 }\sqrt{ 6 } }$

When a square root of an expression is multiplied by itself, the result is that expression

$\frac{ 6\sqrt{ 6 } }{ 6 }$

Cancel out the common factor $6$

$\begin{align*}&\sqrt{ 6 } \\&\approx2.44949\end{align*}$