1. ## Evaluate Expression

I'm rushing through review homework and I came up against one that I can't solve for the same answer the book has.

$\displaystyle \frac{-5^2\times10+10\times2^4}{-5-3-1}$

The book says this evaluates to 10. I am getting something more like $\displaystyle \frac{410}{-9}$

Any ideas what I might be doing wrong? I suspect it's order of operations but I can't nail it.

2. ## re: Evaluate Expression

Without seeing exactly what you've done it's hard to say where you went wrong.

$\displaystyle \frac{-5^2\cdot10+10\cdot2^4}{-5-3-1}=$

$\displaystyle \frac{10\left(2^4-5^2\right)}{-(5+3+1)}=$

$\displaystyle \frac{10\left(\left(2^2+5\right)\left(2^2-5\right)\right)}{-(9)}=$

$\displaystyle \frac{10(9)(-1)}{(-1)9}=10$

3. ## re: Evaluate Expression

Ah, alright, thank you. That makes a lot of sense. I was evaluating each side of the numerator expression first then adding them together (thus the 410). Is this the associative property of mult.?

4. ## re: Evaluate Expression

Doing that, you would have:

$\displaystyle \frac{-250+160}{-9}=\frac{-90}{-9}=10$

Recall: $\displaystyle -5^2\ne(-5)^2$...

5. ## re: Evaluate Expression

And again, that also makes a lot of sense, I did not realize that. So the negative is applied after the 5 is squared? Is this always the case without parentheses or is it particular to the leading term of the expression? Apologies, I am returning to math after a 15 year layoff and I've clearly forgotten some details.

6. ## re: Evaluate Expression

It's an order of operations thing...

$\displaystyle -5^2=-(5^2)=-25$

whereas with $\displaystyle (-5)^2$ the parentheses causes the negative sign to be applied to the 5 first before squaring, so that we have:

$\displaystyle (-5)(-5)=25$

7. ## re: Evaluate Expression

Gotcha. Thanks once more!