Question #91306

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Answer 1 · 2017-02-06T13:32:31

$=12sqrt2xxm^3k^3$

Note one of the laws of indices:

$root(q)(x^p) = x ^(p/q)$

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

So $sqrt (x^10) = x^5" "root3(x^9) = x^3$

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

$324 = 2xx2xx3xx3xx3xx3 = 2^2 xx 3^4$

$64 = 2^6$

Use these factors instead of $324 and 64$

$root(4)(324m^12) xx root3(64k^9)$

$=root(4)(2^2xx3^4xxm^12) xx root3(2^6xxk^9)$

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

$=2^(1/2) xxcolor(blue)(3) xxm^3 xxcolor(blue)(2^2) xx k^3" "larr$ multiply the numbers

$=color(blue)(12) sqrt2xx m^3k^3" "(2^(1/2) = sqrt2)$

Hope this helps?