Question

How do you write ${(4n)^2}$ without exponents?

Answer 1

Hint:
We have a constant which is 4n as the base whose power is given as two. We will have multiple ways to solve this question but we will consider only a few of them. Squaring means multiplying the base with itself twice and the result will be our answer. Answer is required without exponents, that is the answer should not be in the form of a base raised to a unique power on all the terms of the base.

Complete step by step solution:
 According to the question we have to write ${(4n)^2}$ without exponents
At first, we will use the exponential formula
$ \Rightarrow {a^2} = a \times a$
So in the question we have 4n as a in the formula
So we will square 4n and we will get our solution as
$ \Rightarrow {(4n)^2} = 4n \times 4n$
$ \Rightarrow 16{n^2}$
Hence, we will get our solution as $16{n^2}$, which is without exponents.
We can also solve this question in another way as shown billow
$ \Rightarrow 4{n^2} = (4)(4)({n^2})$
$ \Rightarrow 16{n^2}$
Again, we get $16{n^2}$ as our solution for the question.

Note:
We can clearly observe that there are multiple ways to solve this question. All the different ways will be correct if we get our answer as $16{n^2}$ at the end. We also have to be aware of the different exponential formulas because these will be very important for solving these types of equations. The greater the power will be of the base, there will be more ways to reach to the solution. Also when the base is of multiple terms, there will be more ways to solve the question.