Question

i was wondering if anyone could help me on this problem.

expand:
x^-2 (y^2 + 10x)
z^3 (5x + 3z^-4)


First one:

x^-2 (y^2 + 10x)

x^-2 is the same thing as 1/x^2.

Therefore, we have this:

1/x^2 (y^2 + 10x)

Multiply using the distributive property:

y^2/x^2 + 10x/x^2

Add together because you have the same denominator:

(y^2 + 10x)/x^2

And that's as far as we can go on this one!

I'll let you try the second one on your own. Hint: z^-4 is the same as 1/z^4.

I hope this helps.


One other thing about your first problem; if you are to expand and leave it as y^2/x^2 + 10x/x^2, then reduce the second fraction and you will end up with this:
y^2/x^2 + 10/x

I hope this helps.


that was all one problem the stuff on the top has a line between the top and the bottom


Ok, let's approach the problem differently. Since this is all one problem, I'll rewrite it as such:

[x^-2 (y^2 + 10x)] /
[z^3 (5x + 3z^-4)]

Working it out:

[(y^2 + 10x)/x^2] /
[z^3(5x + 3/z^4)] =

[(y^2 + 10x)/x^2] /
[(5xz^3 + 3/z) =

[(y^2 + 10x)/x^2] /
[(5xz^4/z + 3/z)] =

[(y^2 + 10x)/x^2] /
[(5xz^4 + 3)/z] =

[z(y^2 + 10x)] /
[x^2(5xz^4 + 3)] =

(y^2z + 10xz) /
(5x^3z^4 + 3x^2)

This is as far as you can go; I don't see any other way to reduce this further.