How do you simplify #(-2x^2y^3)(3x^4y)#?

2 Answers
MrsRudolph221
Jan 21, 2017

You can remove all of the parentheses and rearrange terms like this:
#-2*3*x^2*x^4*y^3*y#

Explanation:

Now, multiply the numbers, and each variable that is alike:
#-6*x^6*y^4#
Make sure that you apply the Multiply-Add rule for exponents when the base is the same!
A frequently made mistake would be to multiply the exponents, or to forget that "y" is really #y^1# when adding the exponents.

smendyka
Jan 21, 2017

See the entire simplification process below:

Explanation:

First step, rearrange to group like terms:

#(-2 xx 3)(x^2 xx x^4)(y^3 xx y)#

Now, combine like terms using these two rules for exponents:

#a = a^color(red)(1)#
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) +color(blue)(b))#

#-6(x^2 xx x^4)(y^3 xx y^1)#

#-6x^(2+4)y^(3+1)#

#-6x^6y^4#

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