simplifying exponentials?

Question

In this expression:

y^(2a+5) x y^(3a-1) / y^(a-2)

I simplified it down to x^(5a+4)/x^(a-2).
Can I simplify further or is this done?

Sorry when I wrote the question down I used y's instread of x's so that it wouldn't be mixed up with the multiplication sign.

Answer 1

y^(5a+4)/y^(a-2) = y^ ((5a+4)-(a-2)) = y^(4a+6)

since x^a/x^b = x^(a-b)

Answer 2

if by this you mean

(y^(2a + 5) * x * y^(3a - 1))/(y^(a - 2))
(y^((2a + 5) + (3a - 1)) * x)/(y^(a - 2))
(y^(2a + 5 + 3a - 1) * x)/(y^(a - 2))
(y^(5a + 4) * x)/(y^(a - 2))
y^((5a + 4) - (a - 2)) * x
y^(5a + 4 - a + 2) * x
xy^(4a + 6)

however if you meant

(x^(2a + 5) * x * x^(3a - 1))/(x^(a - 2))
(x^(2a + 5) * x^1 * x^(3a - 1))/(x^(a - 2))
(x^((2a + 5) + 1 + (3a - 1))/(x^(a - 2))
(x^(2a + 5 + 1 + 3a - 1))/(x^(a - 2))
(x^(5a + 5))/(x^(a - 2))
x^((5a + 5) - (a - 2))
x^(5a + 5 - a + 2)
x^(4a + 7)

whatever you meant, maybe you can figure out how to actually do it.

Answer 3

= y^[ (5a + 4) - (a - 2) ]
= y^(4a + 6)
= y^[ 2.(2a + 3) ]

Answer 4

Yes you can
In the same way you added exponents when you multiplied, you can subtract exponents when you divide.

x^(5a+4)/x^(a-2) = x^[5a+4 -(a-2)]
= x^(4a + 6)