Question

Simplify a × 3a3b.

A. 6a4b2
B. 2a4b7
C. 4a2b2
D. 3a4b

Answer 1

`Use:a^n\cdot a^m=a^(n+m)\\\\a\cdot3a^3b=3a^(1+3)b=3a^4b\\\\Answer:\boxed{D.\ 3a^4b}`

Answer 2

D.
`3a^4b`

Explanation:

We have:
`a.3a^3b` in order to simplify this expression, we have to apply the rule of the exponents.

This rule says that:

`a^b.a^c=a^(^b^+^c^)`

If you have the same base, the exponents can be added.

We can rewrite the expression
`a.3a^3b` as
`3(a.a^3)b`

Then we have:

`a.a^3=a^1.a^3=a^(^1^+^3^)=a^4`

Finally:

`a.3a^3b=3(a^4)b=3a^4b`

The correct option is D.