Stop with the all-caps and name changes, or seek help elsewhere. You do not appear to be making any effort to learn algebra.
how dare you say that why in the hell do you think I'm on here don't judge me cause i need help to understand how to do the problems Math is my poorest subject for me and i'm trying to receive help not critisim. wow you go on a site for help and they treqt you badly thanks
ALl that said, you just need to see why the rules for adding exponents work the way they do.
a^2 = a*a
a^3 = a*a*a
a^2*a^3 = (a*a) * (a*a*a) = a*a*a*a*a = a^5 = a^(2+3)
So, when you multiply numbers raised to powers, just add the exponents.
Division works the same way, but you subtract powers.
a^5 / a^3 = a*a*a*a*a/a*a*a
and the three a's in the bottom cancel with three of the a's in the top, leaving (5-3)=2,or a^2
Note how this sneakily includes the rule that negative powers in the top can be changed to positive powers in the bottom of a fraction.
a^-3 = 1/a^3 because a^0 = 1. So, a^-3 = a^(0-3) = a^0/a^3 = 1/a^3
Similarly, negative powers in the bottom change to positive powers in the top. 1/a^-3 = a^3
Now, for your problems, it all works together
10a^8 / 7v^3 * 49r^7 / 100a
10a^8 * 49r^7 / 7v^3 * 100a
10 * 7^2 * a^8 * r^7 / 10*10*7 * v^3 * a
Now things start cenceling, and you are left with just
7 a^7 * r^7 / 10 * v^3
If the v or r was a typo, meaning the v is really r, then we have
7 a^7 r^4/10
Just take things one factor at a time, remembering that dividing by a fraction is just the same as multiplying by its reciprocal. All the negative and positive exponents swap places up and down.