Question

How do you simplify ${2^2}{\times2^4}{\times2^6}$?

Answer 1

Hint: In order to solve this question we will first break down all the terms into their simplest form then after it we will multiply all the terms and will get the final answer. Or there is an alternate method of solving this which is first we will have the identity that is “if the base is the same then the powers added” and will solve.

Complete step-by-step solution:
For solving such types of questions we will first break down all the terms to their simplest form, that is we will break ${2^2},{2^4}$ and ${2^6}$.
$\Rightarrow {2^2} = 2 \times 2$
On further solving this we will get:
$\Rightarrow {2^2} = 4$
Now we will similarly solve for:
$\Rightarrow {2^4} = 2 \times 2 \times 2 \times 2$
On multiplying all these terms we will get:
$\Rightarrow {2^4} = 16$
Now we will do same for the remained:
$\Rightarrow {2^6} = 2 \times 2 \times 2 \times 2 \times 2 \times 2$
After finalizing it we will get the:
$\Rightarrow {2^6} = 64$
On assembling all these we will get the final answer,
$\Rightarrow {2^2}{\times2^4}{\times2^6} = 4 \times 16 \times 64$
Now on further solving it we will get:
$\Rightarrow {2^2}{\times 2^4}{\times2^6} = 4096$

Hence the correct answer is $4096$.

Note: Alternate method:
Here is an alternate method of solving these types of questions that is if the base of the multiplicative numbers are same so will be adding all the powers and will get the final answer,
Identity according to expression:
${a^\times a^y \times a^z} = {a^{x + y + z}}$
By applying this identity we will be solving this question:
So according to the question:
${2^2}{\times2^4}{\times2^6} = {2^{2 + 4 + 6}}$
On adding all the powers we will get:
${2^2}{\times2^4}{\times2^6} = {2^{12}}$
On further solving we will get the final answer,
${2^2}{\times2^4}{\times 2^6} = 4096$
So 4096 is our final answer.

As we can see that we are getting the same answer in both the cases. According to me the second method was more easy but you can do it according to your understanding this is simple multiplication but complicated, it is because it is lengthy so it has to be done very carefully.