Question

Could someone help me simplify these radicals with absolute value?

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

Answer 1

`2/x`

Explanation:

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!