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

2 Answers
Mar 3, 2018

Answer:

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

Mar 3, 2018

Answer:

#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 :)