Question

when im dividing exponents do i multiply the bases? example: 6p to the 4th power ➗ 4p to the third power ? would i multiply 6 and 4?

Answer 1

If you have 6p^4/4p^3 you would subtract the powers when dividing the bases so you're answer would be 3p/2. divide the constants(6 and 4) like you would normally would

6p^4=6p*p*p*p
divided by
4p^3=4p*p*p
-------------------
3p/2

Answer 2

No.  The 6 is over the 4.  So no matter what else is in the fraction,
the 6 is divided by the 4.  In other words, that part of the fraction ...
6/4 ... simplifies to 3/2 .

Settle down and let's look at that problem:

You said:          6 p⁴ / 4 p³

I hope you see that this ugly complicated fraction can be written as
the product of two separate fractions.  It's exactly the same thing as

                        6/4  times  p⁴/p³ .

Simplify the first one:     6/4 = 3/2

Simplify the second one:     p⁴/p³ = p

And the original fraction becomes        6p⁴/4p³  =  3/2 p .

=====================================

Now, if you'll stay with me, I want to take you back to the original
problem, and do it a slightly different way:

Even though the original fraction has both numbers and a variable
in it, the question is actually something that you've done hundreds
of times before ... simplify the fraction !

How do you simplify a fraction ?  (Review)  Find a common factor of
the top and bottom, then divide top and bottom by the common factor.

OK.  We have  6p⁴  and  4p³ .

The factors of  6p⁴  are:  1,  2,  3,  6,  p,  p²,  p³, and  p⁴ .

The factors of  4p³  are:  1,  2,  4,  p,  p², and  p³ .

What do we have for common factors ?  I see ' 2 ' and ' p³ ' .

Divide the top by  2p³ :            6p⁴ / 2p³ = 3p

Divide the bottom by  2p³ :      4p³ / 2p³ = 2

Now, after simplifying, the fraction is  (3p/2)  or  (3/2 p) .