Question

Find the value of ${(7)^5}$ .
(A) 12098
(B) 14609
(C) 16807
(D) 3408

Answer 1

Hint: In order to answer this question, as we can see that the given question belongs to the topic of exponents, so we should go through the exponent concept, and then work on the concept of it. We will first elaborate the number if it has some power on it, and then solve for it.

Complete step-by-step solution:
The given expression is related to the exponential and power topic.
A power, also known as an exponent, is a number that represents a repeated multiplication operation. Solving for an exponent (that is, when an exponent contains a variable rather than just a number) normally necessitates the use of logarithms, which come with helpful rules for solving exponent problems.
So, the given expression is: ${(7)^5}$ that means 7 is multiplied 5times by itself.
Now, we will solve the given expression-
$\therefore {7^5} $
$= 7 \times 7 \times 7 \times 7 \times 7 $
$=243 \times 7 \times 7 $
$ = 16,807 $
Hence, the value of ${(7)^5}$ is 16807.
Hence, the correct option is (C).

Note: If we are looking to solve the exponent equation such as ${3^{x + 5}} = {3^{10}}$ , in this case we will ignore the base because exponential rules tells us that in any exponential equation, if the bases are same, then we can equate only the exponents:
$\begin{gathered}
  \therefore x + 5 = 10 \\
   \Rightarrow x = 10 - 5 \\
   \Rightarrow x = 5 \\
\end{gathered} $