Is there any key factor I could remember to help me with these problems.?

Question

The fourth root of 16xy5^5...convert the radical expression to equivalent expressions using radical exponents and simplify if appropriate.

Answer 1

I write em factored.

So I'd write 16xy^5 as:
2*2*2*2*x*y*y*y*y*y

Then, since I'm looking for a 4th root, I can group the same things by 4. (If it were a cube root, I'd group in 3's, square root by 2's etc...)

So [2*2*2*2]*x*[y*y*y*y]*y

That group would be represented by one of it's members, so the group of 2's comes out of the radical as a 2, and the group of y's comes out as a y. What's left, stays inside. So,
4th root of 16x*y^5 would be
2*y*4th-root(x*y)

The notation's not quite right, but that's my best guess at an explanation given the phrasing of the question ;-)

Answer 2

What is y5^5? I think you need parentheses.

The fourth root of 16xy^5 is done base by base: 4th root of 16 is 2, 4th root of x is 4th root of x, 4th root of y^5 -- that's the interesting part, divide 5 by 4 getting 1 remainder 1, and the first 1 gives you y outside the radical sign and the remainder gives you y^1 INSIDE the radical, so you end up with 2y • 4th rt (xy).

Answer 3

I cannot tell what the function is.
(16xy^5)^(1/4)???
If that is it, then you get (16)^(1/4)*(x^1/4)*(y^5)^(1/4)
= (2^4)^(1/4)*(x^1/4)*(y^5/4) = 2*(x^1/4)*(y^1)*y^(1/4)
2*(xy)^(1/4)*y