What is #36y^4*.5y^2#?

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Please explain, thank you!

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Answer 1 · 2018-03-26T22:58:03

The simplified answer is #18y^6#.

Since multiplication is commutative (meaning #3*5# is the same as #5*3#), you can move around the terms, and then combine the constants.

To simplify the #y# terms, use the law of exponents:

#x^color(red)m*x^color(blue)n=x^(color(red)m+color(blue)n)#

Now here's our expression (I added color-coding for each term so it's easier to follow:

#color(white)=36y^4*0.5y^2#

#=color(red)36*color(green)(y^4)*color(blue)0.5*color(magenta)(y^2)#

#=color(red)36*color(blue)0.5*color(green)(y^4)*color(magenta)(y^2)#

#=color(purple)18*color(green)(y^4)*color(magenta)(y^2)#

#=color(purple)18*color(brown)y^(color(green)4+color(magenta)2)#

#=color(purple)18*color(brown)y^color(brown)6#

#=color(purple)18color(brown)y^color(brown)6#

This is the simplified result. Hope this helped!

Answer 2 · 2018-03-26T22:58:24

The answer is #18y^6#, with the explanation below.

A good way to understand what's going on here is to write out all of the multipliers (I'm going to avoid expanding all of the exponents):

#36y^4*0.5y^2=36*y^4*0.5*y^2#

Now, we can start grouping like elements:

#(36*0.5)(y^4*y^2)=18(y^4*y^2)#

As you may or may not know, when you multiply two exponents together with the same base, you simply add the values of the powers together. This way:

#18(y^4*y^2)=18(y^(4+2))#

#color(red)(18y^6)#