Question

How do you simplify `2^2 \cdot 2^4 \cdot 2^6`?

Answer 1

See a solution process below:

Explanation:

Use this rule for exponents to simplify the expression:

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

`2^color(red)(2) xx 2^color(blue)(4) xx 2^color(green)(6) => 2^(color(red)(2) + color(blue)(4) + color(green)(6)) => 2^12`

`2^12` in its simplest form is 4096

Answer 2

`2^12`

Explanation:

It's easier to think about the problem by writing it out like this:
`(2*2)*(2*2*2*2)*(2*2*2*2*2*2)`
Count the number of twos,
`2^12`
while it helps to think about it that way, the easiest way to solve it is to just add the exponents.
`2^2*2^4*2^6`
`2+4=6`
`6+6=12`
`2^12`
I hope this helps :)