Could someone help me simplify these radicals with absolute value?

Question

I need to simplify #sqrt((36x^4#)/#sqrt((9x^6#)

After simplifying, I get, [(|6|)(|x^2|)]/[(|3|)(|x^3|)] How would I simplify further

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Answer 1 · 2018-02-20T23:21:23

#2/x#

So you have #(6x^2)/(3x^3)# you firstly divide the numbers, so #6/3=2#. Then you use the properties of exponents. For this problem this one applies:

#(x^a)/(x^b)=(x^(a-b))#

Here, your a is 2 and your b is 3, so is becomes #x^(2-3)# which simplifies to #1/x# then #2×(1/x)=(2/x)#. Yay!