Indices: Can anyone help me?

Question

(5y^3)^1/2


Thank you. If you could give a brief explanation that would be appreciated, although I might try and work it out myself with the answer if you like.

Answer 1

The rules to remember here are:
(a^b)^c = a^(bc), and
(ab)^c = (a^c)(b^c)

So apply that here, we have:
[ 5^(1/2) ] [ (y^3)^(1/2) ] =
5^(1/2) y^(3/2)

Answer 2

By indices you mean exponents?

y^3 means y times y times y, 3 y's.

(stuff)^1/2 means square root. So

(5y^3)^1/2 = √(5y^3) = | y | √(5y)

Notice √(y²) is not y but is | y |, since √(-3)² = √9 = 3 and that's not -3.