How do you add exponents, e.g. n^2 + n^2?

Question

I get stuck on this problem when it is time to add:

9y^4/x^-2 + (x^-1/y^2)^-2

Steps:
9x^2y^4 + x^2/y^-4
9x^2y^4 + x^2y^4

=10x^2y^4?

This question is still confusing to me, because it seems like every solution to the equation does x^2 + x^2 = x^2, instead of x^2 + x^2 = 2x^2.

Answer 1

First, I presume you really mean "How do you add quantities with exponents IN them?"

You seem to be asking TWO things, in fact :

1. In your heading, n^2 + n^2 is merely adding two IDENTICAL things. The result is simply 2 n^2. However, were it n^2 + m^2 (and only that, with quite independent variables ' n ' and ' m '), there's no way that you could combine them in real terms. (You could of course write them as (n + i m)(n - i m), employing ' i ', the square root of - 1, but I don't think you were after that.)

2. What you wanted to know about in your subsequent contextual "explanation" (which was in fact something different) was how to add together mixed expressions in powers of more than one variable. For that, what you did appears to be just fine. After you'd unscrambled the various " / " and " ^(-p) " symbols, you found that you were indeed adding two multiples of EXACTLY the same combination of variables; and I agree, that was CORRECT, and the answer should indeed be 10x^2y^4.

[ I only have one comment : for clarity, I prefer to see parentheses or brackets around any power that isn't a single (positive) integer or single (positive) variable, just as a fail-safe practice. It would not be strictly necessary, were everyone to follow the order of operations properly when writing their expressions; but I have seen far too many examples recently in which that was simply not done, in questions posed on Yahoo! Answers, as well as in many of the responses. ]

Live long and prosper.

POSTSCRIPT : Your "additional details," added a FULL 4 DAYS AFTER your original question ( ! ), can only serve to confuse your responders still further, since you assert something that we all:

(i) have NO possible chance of checking, concerning your own experiences, and

(ii) must very seriously doubt, since it seems manifestly WRONG, at least in my experience!

Here is how those "additional details" were displayed:
--------------------------------------------------------------------------
Additional Details
4 hours ago
This question is still confusing to me, because it seems like every solution to the equation does x^2 + x^2 = x^2, instead of x^2 + x^2 = 2x^2.
4 days ago - 4 days left to answer. - 8 answers - Report Abuse
--------------------------------------------------------------------------

You MUST be MISTAKEN in asserting that "every solution to the equation does x^2 + x^2 = x^2." Can you please tell us where this assertion comes from, and try to express what concerns you more explicitly and understandably? Thank you.

Answer 2

I would guess that you are writing....

9x to the second power y to the 4th power plus x to the second power y to the 4th power?????

this would be 10x to the second power plus 2y to the 4th power............its kind of hard on the computer.

The thing about exponents is when you add you only add the coefficent which is the number in front of the variable which is the letter.

In your question you have as an e.g. n^2 +n^2 this would equal 2n^2.

So...if you have 2x plus 2x then your answer would be 4x.

if you had 2x to the 3rd power plus 6x to the 3rd power then your answer would be 8x to the 3rd power.

If you have exponents that are not similar then you do not add them. You just keep them as they are.

An example would be if you have 2x plus 2x to the 3rd power then you just keep it the way it is because it is simplified. I hope that this helps.

Have a nice night!

Answer 3

You can't add exponents. To add terms, you can only combine them if they're the same form. E.g. x^2*y^2 + 3x^2*y^2 = 4x^2*y^2, but x^2*y^2 + x^2*y^4 cannot be combined.

Answer 4

n^2 + n^2 = 2n^2 you don't add or do anything to exponents.. it's just the coefficients that change

n^2*n^2 = n^4 is when you add the exponents... (multiplication)

(n^2)^3 = n^6 is when you mulitply the exponents

Answer 5

I raised my daughter as a single determine and by way of the time she became into 9 years previous, she went everywhere she had to bypass, alongside with stay shows to confirm Alice in Chains, Marilyn Manson, 9 Inch Nails, weapons 'n Roses, etc., dances, fairs, procuring, all in our interior of reach city and likewise Chicago, long island, and London. especially situations she went together with her friends, especially situations not. yet every time she went with me. That became into the deal. definite, you may bypass, yet i'm tagging alongside. She balked in the beginning up, yet quickly time I grew to alter into the cool mom who knew all her friends and that they knew me and we had great situations, all and sundry at the same time. Their mothers and dads additionally liked the reality that i became into there keeping an eye fixed, from a distance, on their little ones. i don't recommend this attitude for each determine, yet for me, it worked using fact there became into no way i became into letting my angel available on my own between the wolves.

Answer 6

so you mean a^2+b^2

a^2+b^2=(a+b)^2-2ab

if n^2+n^2, then it leaves us 2n^2!

so 9y^4/x^-2+(x^-1/y^2)^-2=
=9y^4x^2+(1/xy^2)^-2=
=9(xy^2)^2+(xy^2)^2=
=10(xy^2)^2
=10x^2y^4

Answer 7

Your answer is correct!

As long as all of the powers match, you are okay here.

Answer 8

If they have the same bases, you add them.

Answer 9

u r absolutely correct