SOLUTION: Which expression represents the simplet form of (2x^3y^4)(4x^2y^5)

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Question 65885: Which expression represents the simplet form of (2x^3y^4)(4x^2y^5)
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

Which expression represents the simplest form of (2x3y4)(4x2y5)

(2·x3·y4)·(4·x2·y5)

Write the x3 as x·x·x
Write the y4 as y·y·y·y
Write the x2 as x·x
Write the y5 as y·y·y·y·y

(2·x·x·x·y·y·y·y)·(4·x·x·y·y·y·y·y)

We don't need the parentheses since everything
is multiplied

2·x·x·x·y·y·y·y·4·x·x·y·y·y·y·y

Rearrange it so that the numbers are together 
and the like letters are togetner

2·4·x·x·x·x·x·y·y·y·y·y·y·y·y·y

Multiply the 2 by the 4 and get 8
Write the x·x·x·x·x as x5
Write the y·y·y·y·y·y·y·y·y as y9

So you end up with 8x5y9

Here's an easier way which amounts to doing the same
thing:

(2x3y4)(4x2y5)

Multiply the 2 by the 4, get 8
Add the exponents of x, which are 3 and 2. 3+2 = 5, so write x5
Add the exponents of y, which are 4 and 5, 4+5 = 9, so write x9

Answer: 8x5y9

Edwin