Answer: Understanding Exponents: Inside vs Outside Brackets

[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)

 

[cristo]

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

 

[Styx]

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

but that would make the answer -625, not 625

 

[cristo]

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.

 

[Styx]

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

 

[cristo]

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