Math help Explanation please!

need help on a few math problems
1) (y2)^-4- y8
2) (4y^4)^3/2
3)2n/4n^1/2

I assume that you mean:

Problem 1)
.. ( y^(2) )^(-4) - y^(8)
= y^( 2 * (-4) ) - y^(8)
= y^(-8) - y^(8)
= 1/y^(8) - y^(8)
= ( 1 - y^(8)*y^(8) ) / y^(8)
= ( 1 - y^(8+8) ) / y^(8)
= ( 1 - y^(16) ) / y^(8)

Problem 2)
.. ( 4y^(4) )^(3/2)
= (4)^(3/2) y^( 4 * (3/2) )
= (2)^(3) y^(2*3)
= 8 y^(6)

Problem 3)
.. 2n / (4n)^(1/2)
= 2n / [ (4)^(1/2) (n)^(1/2) ]
= 2n / [ 2 (n)^(1/2) ]
= n^(1) / (n)^(1/2)
= n^(1) * (n)^(-1/2)
= n^(1-1/2)
= n^(1/2)

1) -16y
2) 4y^12/2 = 4y^6
3) 1/2n^1/2 = n (halfs cancel)