Question

What is the value of ${{32}^{4}}$ ?

Answer 1

Hint: The given mathematical term is an expression raised to a certain power. Now, the value of these terms whose powers are integers can be easily calculated by multiplying the term with itself. The number of times that we will multiply this term with itself will be equal to the positive integer at the power of that expression.

Complete step by step solution:
The expression given to us in the problem is: ${{32}^{4}}$. Let us now assign some terms that we are going to use later. Let us denote the term ‘x’ for the given expression such that we need to find the value of ‘x’ .
According to our notation, we have:
$\Rightarrow x={{32}^{4}}$
The above expression can be simplified by writing the term on which power is operated (in this case, 32) the number of times equal to its power. Mathematically, this could be written as:
$\Rightarrow x=32\times 32\times 32\times 32$
Now, on further simplifying our equation by finding the product of the terms in the Right-Hand Side of the above equation by splitting them up into groups of two, we get the final result as:
$\begin{align}
  & \Rightarrow x=1024\times 1024 \\
 & \therefore x=1048576 \\
\end{align}$
Thus, we get the final value of ‘x’ as 1048576 .
Hence, the value of ${{32}^{4}}$ comes out to be 1048576.

Note: Whenever there is a long and lengthy calculation in our solution, we should always cross check our solution for any possible mathematical errors. Also, if the power in the expression is a negative integer, we can reciprocate the term so that its power becomes positive. This will make our problem easier to solve.