# Thread: simplifying an expression with exponents, such that x=-1

1. ## simplifying an expression with exponents, such that x=-1

If I want to simplify the following expression such that x= -1:

-9x2 - x + 1
___________
x3 + x

How do I input the value of -1 into -9x2?

like this -9(-1)2 which simplifies to -9(1) which equals -9

or like this -9(-12) which simplifies to -9(-1) which equals positive 9

I ask this because I know that exponents only apply to the value or parenthetical expression right next to it. In the former case, (-1) times (-1) is positive 1. In the latter case, the square only applies to the 1 and not to the minus sign which is then left over after the 1 is squared. So, this yields a -1.

So, which way is right??

2. ## Re: simplifying an expression with exponents, such that x=-1

$\displaystyle x^{2}$ is shorthand notation for $\displaystyle x$ multiplied by $\displaystyle x.$
Substitute $\displaystyle x=-1$ and you get $\displaystyle x^{2}=x.x=(-1).(-1)=1$

3. ## Re: simplifying an expression with exponents, such that x=-1

remember your order of operations?

$\displaystyle -9(-1)^2$

evaluate exponents first ...

$\displaystyle -9(1)$

then multiply ..

$\displaystyle -9$

4. ## Re: simplifying an expression with exponents, such that x=-1

Originally Posted by skeeter
remember your order of operations?

$\displaystyle -9(-1)^2$

evaluate exponents first ...

$\displaystyle -9(1)$

then multiply ..

$\displaystyle -9$
Actually, the first letter in PEMDAS (which I first learned as "Please Excuse My Dear Aunt Sally") is "P" which stands for "parentheses". That is why it is specifically (-1)^2= 1, not -(1^2)= -1.