Question

x^18y^12 + x^9y^8 over x^3y^4
If x=0 and y=0, which of the following is a simplified version of the expression above?
a. x^9y^5
b. x^24y^16
c. x^6y^3 + x^3y^2
d. x^15y^8 + x^6y^4

Answer 1

My guess is that no one has answered this question is because if x=0 and y=0 then the equation amounts to 0. However, looking at the answers and ignoring what it says about x and y being 0, answer d is correct. If you like, I can show you how to work it out.

Answer 2

Yes ,please. I would really enjoy knowing how to work this out rather than just knowing the answer.

Answer 3

ok...forgetting the x=0, y=0 thing (which doesn't make sense) I'll work out how to simplify it. Your equation is\[\frac{x^{18}y^{12}+x^9y^8}{x^3y^4}\]Is that correct so far?

Answer 4

yes

Answer 5

Ok, that can be rewritten as:\[\frac{x^{18}y^{12}}{x^3y^4}+\frac{x^9y^8}{x^3y^4}\]Good so far?

Answer 6

Yes, so far.

Answer 7

Ok. The exponent rules state that if you're dividing exponents with like bases, you just subtract the bottom exponent from the top exponent. This simplifies things down to:\[{x^{15}y^8}+x^6y^4\]All I did was subtract exponents with like bases.

Note that if you were to subtract the exponents and end up with a negative value, you would make it positive and move it to the numerator.

Answer 8

Mmhmm I see.

Answer 9

If I went too fast on the last part I can probably show you a simpler example to make the point.

Answer 10

My guess is that the x=0 and y=0 should have read:\[x \neq 0, y \neq 0\]

Answer 11

Which would make more sense.

Answer 12

Yes! That is exactly what they were, I just could not figure out how to put them in...

Answer 13

Just use the equation editor if you need to...it has a symbol in there for "not equal".