Question

Which expression is equivalent to \[\left( {{9^2}} \right)\]?
A) -81
B) \[\dfrac{1}{{81}}\]
C) 81
D) none of these

Answer 1

Hint: Here in this question we have given a number. The terms involved in this term are in exponential form. The exponential form is written in the form of the numeral and then we have to apply the arithmetic operations. Hence on further simplification, we obtain the required solution for the question.

Complete step-by-step solution:
The exponential number is defined as the number of times the number is multiplied by itself. It is represented as \[{a^n}\], where a is the numeral and n represents the number of times the number is multiplied.

Now consider the question, the question is the form of exponential and we have to expand it and we have to write the numeral form and we have to compare the obtained solution to the given options.
On considering the given question we have
\[ \Rightarrow \left( {{9^2}} \right)\]
This can be written as
\[ \Rightarrow 9 \times 9\]
We write the number 9 twice because the power of the number 9 is 2. We apply the multiplication operation between these two numbers.
On multiplying we have
\[ \Rightarrow 81\]
Hence we have solved the above expression and found the solution.
Therefore the option c) is the correct one.
therefore 81 is equivalent to \[\left( {{9^2}} \right)\]

Thus the correct answer is option ‘C’.

Note: The exponential number is defined as the number of times the number is multiplied by itself. It is represented as \[{a^n}\], where a is the numeral and n represents the number of times the number is multiplied. For the exponential numbers we have the law of indices and by applying it we can solve the given number.