Math 10 question?

Question

Text Book: Mathpower Ten Western Edition

The question is on powers and exponents. If you could help explain the steps to me in an easy-to-follow way, that would be great and well appreciated. Thanks in advance.

I am going to put the powers (little numbers) in the square brackets. I hope you don't get confused. The -a[3] over the -(b[2]) is what you multiply the first part of the question with. It just looks confusing because the spacing is messed up.

Question:
4a[4]b[3] -a[3]
----------- x -------
a[5]b[6] -(b[2])

Answer:
4a[2]
------
b[5]

Answer 1

first you have to know the idea of adding or subtracting powers
in multiplying we add powers and in division we subtract the powers
so we will add and subtract the powers as follow:
4a[4]b[3] -a[3]
----------- x -------
a[5]b[6] -(b[2])

the negative signs will be cancelled
4a[4]b[3] a[3]
----------- x -------
a[5]b[6] (b[2])


=4 a[ 4+3-5] * b[3-6-2]
=4 a [2] * b[-5]
= 4a[2] /b[5]

Answer 2

OK, I'll help with this.. but you have to promise to really learn it and understand it. I don't give answers out.. I want to help people learn it.

First step I would do is to get rid of the negatives on the top and bottom of the term on the right. You do that by multiplying both by -1.

Next, you can combine "like" terms going across (all the "a"s and all the "b"s). Since you're multiplying all the terms, the order doesn't matter. Remember, when you multiply exponents, you end up adding the powers. So for the numerator of the entire equation, that gives you:

4a[4] x a[3] x b[3] = 4a[7]b[3] ---> (the a[4] times the a[3] gives you a[7].. and you keep the 4 there.. nothing happens with the b[3] yet)

Denominator gives you:

a[5] x b[6] x b[2] = a[5]b[8] ---> (b[6] times b[2] gives you b[8].. nothing happens with the a[5] yet)

This now gives us:

4a[7]b[3]
-----------------
a[5]b[8]

Now, when you divide exponents, you end up subtracting the powers. Again, since it's all multiplication (and division, which is related), you can mix the order up however you like. So, when you divide out the "a" terms, the exponents are subtracted.. so that makes it a[7]/a[5] = a[2]. For the "b" terms, same thing: 8-3=5 (In this case you could've done 3-8=-5, which also works.. review what a negative exponent means). So, putting it all together:

4a[2]
-------
b[5]

The 4 stays put since we didn't get rid of it anywhere along the way. Basically, we combined the like terms going across, then we canceled out (or divided out, or "reduced") the like terms in the division problem.

I hope that helped.. let me know if you have more questions..

Answer 3

They are all multiplication so you can forget about the "x"

4a^4b^3(-a^3)/a^5b^6(-b^2)

Combining like terms and canceling the -'s:
4a^7b^3/a^5b^8

Do the division:
4a^2/b^5

Answer 4

ookk...

whats the question?

Answer 5

I didn't understan ur question...sorry!!!