# Question #91306

Feb 6, 2017

$= 12 \sqrt{2} \times {m}^{3} {k}^{3}$

#### Explanation:

Note one of the laws of indices:

$\sqrt[q]{{x}^{p}} = {x}^{\frac{p}{q}}$

In words this will say " to find a root, divide the index by the root "

So $\sqrt{{x}^{10}} = {x}^{5} \text{ } \sqrt[3]{{x}^{9}} = {x}^{3}$

It is useful to write the numbers as the product of the prime factors.

$324 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 = {2}^{2} \times {3}^{4}$

$64 = {2}^{6}$

Use these factors instead of $324 \mathmr{and} 64$

$\sqrt[4]{324 {m}^{12}} \times \sqrt[3]{64 {k}^{9}}$

$= \sqrt[4]{{2}^{2} \times {3}^{4} \times {m}^{12}} \times \sqrt[3]{{2}^{6} \times {k}^{9}}$

Now divide each index by the root you want to find.

$= {2}^{\frac{1}{2}} \times \textcolor{b l u e}{3} \times {m}^{3} \times \textcolor{b l u e}{{2}^{2}} \times {k}^{3} \text{ } \leftarrow$ multiply the numbers

$= \textcolor{b l u e}{12} \sqrt{2} \times {m}^{3} {k}^{3} \text{ } \left({2}^{\frac{1}{2}} = \sqrt{2}\right)$

Hope this helps?