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?