Question

Expressed in simplest form,(3x^3)(2y)^2(4x^4) is equivalent to

Answer 1

Explanation:

3
`x^(3)`
`(2y)^(2)`4
`x^(4)`

So I wrote down exactly above how the eq. is put in the question, note that the 2y is the only coefficient that is inside of the parenthesis, I hope that is how the question is asked. The 3 and 4 coefficient are NOT part of the exponential part.. is my point.. which will make a big difference if they were.

anyway

3
`x^(3)`4
`y^(2)`4
`x^(4)`

48
`y^(2)`
`x^(3)`
`x^(4)` ( b/c the x bases are the same we can just add the exponents)

48
`y^(2)`
`x^(3+4)`

48
`y^(2)`
`x^(7)` ( this is your answer )

side note: an important learning point that was implied above is that you could rewrite the expression as 48
`y^(2)`
`x^(2)`
`x^(2)`
`x^(2)`
`x^(1)`... why would you want to write it that way? b/c often a square is needed to make a problem work out easier.

as in Cos^2(Ф) + Sin^2(Ф) = 1 but that's another question L :P

(if you're read this far.. good for you.. if it's the 1st time you've heard of that rule for exponents then ask your teacher / professor if I can have 1/2 of their pay since I am doing their job :D )