How do you simplify $2^{2} \cdot 2^{4} \cdot 2^{6}$ $2^2 \cdot 2^4 \cdot 2^6$ ?

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How do you simplify $2^{2} \cdot 2^{4} \cdot 2^{6}$ $2^2 \cdot 2^4 \cdot 2^6$ ?

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Answer 1 · 2018-03-03T16:20:37

See a solution process below:

Explanation:

Use this rule for exponents to simplify the expression:

$x^{a} \times x^{b} = x^{a + b}$ $x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))$

$2^{2} \times 2^{4} \times 2^{6} \Rightarrow 2^{2 + 4 + 6} \Rightarrow 2^{12}$ $2^color(red)(2) xx 2^color(blue)(4) xx 2^color(green)(6) => 2^(color(red)(2) + color(blue)(4) + color(green)(6)) => 2^12$

$2^{12}$ $2^12$ in its simplest form is 4096

Answer 2 · 2018-03-03T16:23:01

$2^{12}$ $2^12$

Explanation:

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

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