Divide....?

Question

m to the 8th power n to the 6th power divided by m to the 4th power and n to the 2 power

I can't figure out how to do this...I see someone else posted this previously but there is only an answer and I would like for someone to explain it to me so I can understand how to do this...Thanks so much.

Answer 1

m^4 (means m to the 4th)

so...

m^8 * n^6
--------------- (divided by)
m^4 * n^2

= m^4 * n^4

You subtract the powers when you divide from each of the like variables.

Answer 2

......m⁸n⁶
---------------
.....m⁴n²

this is short notation for you have 8 m's on top and 6 n's rather than writing out m & n eight and six times, and you have 4 m's and 2 n's on the bottom the long way would have been to write it like this:

(mmmmmmmm nnnnnn) over (mmmm nn)
now you can remove an m from the top for every m on the bottom and the same with the n's leaving you with m⁴( 4 m's OR mmmm) on top and n⁴( 4 n's OR nnnn).

m⁴n⁴ is your answer

the short cut to all of this would be to subtract the m powers and n powers 8-4= 4 for m and 6-2= 4 for n and write the letters with their appropriate powers.

Answer 3

division and multiplication with powers
if bases are same, while multiplying add the powers and while dividing subtract the powers
a^x * a^y = a^(x+ y)
a^x/a^y = a^(x - y)

(m^8)(n^6)/(m^4)(n^2) = m^(8 -4)(n^(6 - 2)
= m^4 n^4

Answer 4

Isn't the answer m^4n^4?

IF I'm recalling that correctly, then to split the equation to see how

(m^2)^4 / (m^2)^2 times (n^2)^3/ (n^2)
cancel out
(m^2)^2 times (n^2)^2

Answer 5

m^8 * n^6 / m^4 * n^2
=
m^4 * n^4

why? because you have
(m*m*m*m*m*m*m*m / m*m*m*m) * (n*n*n*n*n*n / n*n)

Hope this helps.
.