Ummm..messed uo the first one, retry Are you math smart?

Question

Are you math smart?
ok, I have a problem I have been trying to simplify, I THINK I have the answer, but I am not sure. Could you please simplify this? (and NO this is not my homework, I just want to be able to solve this sort of problem.Thank you
x^-5w^3/w^2z^-2

Answer 1

Anywhere you see a negative exponent, you can put it on the opposite side (move from top to bottom or bottom to top) and make the exponent positive. So first rewrite this as

w^3z^2 / x^5w^2

Now w^3 = w*w*w and w^2 = w*w, so you can cancel out 2 of the w's, which leaves one on the top. Note that when the bases (w) are the same, you can subtract the exponents when you divide. w^3/w^2 = w^(3-2) = w^1 = w

Nothing else besides the w's cancel, so you're done.

wz^2/x^5

Answer 2

Just to make sure I got this right, I'll rewrite:

((x^-5)*(w^3)) / ((w^2)*(z^-2))

1) A negative power indicates an inverse (e.g., (x^-5) = 1/(x^5), also 1/(z^-2) = 1/ (1/(z^2)) = z^2

((z^2)*(w^3)) / ((w^2)*(x^5))

2) A positive power in the denominator can be replaced by the negative power in the numerator (this is rule 1 applied the other way around), e.g., 1/(w^2) = (w^-2)

((z^2)*(w^3)*(w^-2)) / (x^5)

3) When multiplying the same variable, you can add the powers, as in (y^a)*(y^b)=y^(a+b)
Here, we have (w^3)*(w^-2)=w^(3-2)=w^1=w

(z^2)*w / (x^5)

4) Reapply rule 2 to 1/(x^5) = (x^-5), and rearrange the order of the variables (rearranging factors does not change the product):

(z^2)*w*(x^-5)
(x^-5)*w*(z^2)

Answer 3

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Answer 4

x^-5w³/w²z-²
Solution: x^-5w over z-²
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