Please someone can explain multiplying monomials in "English"?

Question

sample problem:a^5(a)(a^7)

please show all steps and dictates steps in words!

Answer 1

When you have the same bases (your bases are the a's)
and they are multiplied together (like in your example)
all you do is add the exponents (the 5, the 1, the 7)

***The 1 comes from a^1=a

and keep the base

so the answer in the end will be
a^13

Answer 2

a = a^1 (by definition)
a^5 = a*a*a*a*a (again, by definition)
a^7 = a*a*a*a*a*a*a (again, by definition) Then
(a^5)(a)(a^7) =
(a*a*a*a*a)(a)(a*a*a*a*a*a*a) =
a*a*a*a*a*a*a*a*a*a*a*a*a = a^13 (13 = 5+1+7)

In general
(a^b)(a^c) = a^(b+c)

HTH ☺


Doug

Answer 3

just add the exponents. in your example

a^13