Which simplifying method should be used to simplify 2x^2y^2 times 5xy^4?

[Spitfire]

Hello,

I have already studied first year mathematics but I am doing some basic revision incase I missed anything,
(I skipped two grades and am thus missing some small simple things I should know)

When simplifying the single term expression,
2x^2y^2 times 5xy^4

my initial thought was they cannot be further simplified since they are two different expressions
Would I treat them as if they where in brackets, thus =10 times 2x^4 times 10y^12 times x^3y^6
would I treat them as indeviduals thus = 2x^2y^2 times 5xy^4

I know this is simple but I confused me.
Thank for any help :D

 

[MarkFL]

Hello, Spitfire64! (Wave)

We are given to simplify:

\(\displaystyle 2x^2y^2\times5xy^4\)

Now, we should observe, that this is the same as:

\(\displaystyle 2\times x^2\times y^2\times5\times x\times y^4\)

And the commutative property of multiplication allows us to write this as:

\(\displaystyle 2\times5\times x^2\times x\times y^2\times y^4\)

Now, let's get rid of the unneeded multiplication symbols (and use $2\times5=10$):

\(\displaystyle 10x^2xy^2y^4\)

Now, a property of exponents is:

\(\displaystyle a^ba^c=a^{b+c}\)

Can you finish? :)