# Exponets messing me up

1. May 19, 2007

### Styx

This is probably a very easy question but it is messing me up.

(-y^2)^2 = (-y)^4

but

(-y^2)^3 = (-y^6)

why does one exponent need to be inside the brackets and the other outside?

Example: (-5^2)^2 = 625 = (-5)^4

(-5^2)^3 = -15625 = (-5^6)

2. May 19, 2007

### cristo

Staff Emeritus
You really need to move your parentheses to avoid amibiguity; your first line should really read -(y2)2=-(y4)

3. May 19, 2007

### Styx

but that would make the answer -625, not 625

4. May 19, 2007

### cristo

Staff Emeritus
Sorry, I read it wrong. Well, in that case, you need more parentheses, since -x^2 is very ambiguous; I would take it to mean -(x^2). You should write ((-y)^2)^2, which is equal to (-y)^4, using the correct exponent rule.

5. May 19, 2007

### Styx

Ok, so ((-y)^2)^3 = (-y)^6

Last edited: May 19, 2007
6. May 19, 2007

### cristo

Staff Emeritus
Yes. Notice that it is also equal to y^6 if you square the inside bracket first, since (-y)^2=y^2