Question

Can someone PLEASE explain how to simplify square roots with variables and eexponents in them?? I'd also be thankful if you explained step-by-step how to
solve (16x^4)^3/2 and how to simplify 3y^4/3 times 3yx^1/2? I have to do a retake on my math test and I REALLY need help!

Answer 1

X^a/b is  $\sqrt[b]{x^a}$ . The way I memorise that is x^1/3 is the cubic root of x. Do you get it? In that case, x is raised to a power of 1 and the cubic root is practically has a power of 3.
In your example, 

$\sqrt[ \frac{3}{2} ]{16 x^4}$ is practically square rooting each term then cubing them individually. Remember when square-rooting any index you halve it. I'll elaborate:

$\sqrt{x^4}$ = $x^{2}$
$\sqrt{16}$ = 4
Then cube each,
$4^3$ = 64 
and $( x^{2} )^3$ = $x^{6}$

As for the 2nd part: you must use the rules of indices.
$x^{a} * x^{b} = x^{a+b}$
So breaking the question up:

3 * 3 = 9
$x^{ \frac{1}{2} }$ stays as is since the 2nd term does not contain x
now: 
$y^{ \frac{4}{3} } * y^{1} = y^{ \frac{4}{3} + 1 } = y^{ \frac{4}{3} + \frac{3}{3} } = y^{ \frac{7}{3} }$
This makes your final answer look like this:
$9 x^{ \frac{1}{2} } y^{ \frac{7}{3} }$

I hope that helped and good luck in your test!