Question

Write $128$ as a power of $2$.

Answer 1

Here we have $128$ which has to be expressed in powers of $2$. So by factoring $128$ with the help of $2$ we can identify the number of $2$’s required to divide or factorize $128$ completely such that the number of $2's$ would also represent the power by which $128$ can be expressed.

Complete step by step solution:
Given, $128.......................\left( i \right)$
Now we need to express (i) in terms of the power of $2$. For that we have to factorize $128$ with the help of 2.Now we know that in $128$ the one’s place is occupied by $8$ which is a multiple of $2$.It implies that $128$ is fully divisible by $2$ giving no remainder. So it implies we can divide $128$ with $2$ until we get the number $1$. Also by counting the number of $2's$ needed to reach the number $1$ we can write the power in terms of that number.So dividing (i) with $2$ till it’s not possible to divide:
$\dfrac{{128}}{2} = 64..................1 \\\ \Rightarrow \dfrac{{64}}{2} = 32....................2 \\\ \Rightarrow \dfrac{{32}}{2} = 16....................3 \\\ \Rightarrow \dfrac{{16}}{2} = 8......................4 \\\ \Rightarrow \dfrac{8}{2} = 4.......................5 \\\ \Rightarrow \dfrac{4}{2} = 2.......................6 \\\ \Rightarrow \dfrac{2}{2} = 1.......................7 \\\$
So on observing the above steps it’s clear that the number $2$ is required $7$ times for the complete division of $128$. Such that the above described steps can also be written as shown below:
$128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$\Rightarrow 128 = {2^7}.........................(ii)$
$\therefore \;128 = {2^7}$

Therefore the representation of $128$ as power of $2$ is given as ${2^7}$.

Note: Exponential notation is mainly used to represent a bigger number in terms of product of many factors, which makes it easier for handling bigger numbers. The above mentioned question can also be done by ‘Single Division Method’ where all the division steps are performed in one single step rather than different steps as shown above.