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June 27, 2016
Posted by **JOSH** on Saturday, December 17, 2011 at 6:12pm.

- Algebra -
**drwls**, Saturday, December 17, 2011 at 6:26pmStop with the all-caps and name changes, or seek help elsewhere. You do not appear to be making any effort to learn algebra.

- Algebra -
**Ashley A.**, Saturday, December 17, 2011 at 6:34pmhow dare you say that why in the hell do you think I'm on here dont 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 recieve help not critisim. wow you go on a site for help and they treqt you badly thanks

- Algebra -
**drwls**, Saturday, December 17, 2011 at 6:40pmYou're welcome

- Algebra -
**Steve**, Saturday, December 17, 2011 at 11:30pmALl 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.