Question

If $ {x^m} = {x^n} $ , then the value of m is
A) > n
B) = n
C) < n
D) Cannot be determined

Answer 1

Hint: As there is ‘equal to’ sign, the given statement will be called as an equation. We can observe right and left side of this equation and observe which will be the correct value of m amongst the given options. For equal bases the powers will also be equal.

Complete step-by-step answer:
We have been given an equation:
 $ {x^m} = {x^n} $
And we need to find the value of m in terms of n.
We can see that on both the sides of the given equation, the base number is x i.e. the base of both the powers are the same.
The relationship between the powers in such a case will be the same as that between their bases.
So if $ {x^m} = {x^n} $
 $ \Rightarrow m = n $
Therefore, the correct value of m for the given equation is that it is equal to n and the correct option is B).
So, the correct answer is “Option B”.

Note: Remember that the sign between the powers of the same bases is totally dependent on the sign between their bases. Other options will be valid if:
 $
  {x^m} > {x^n} \Rightarrow m > n \\
  {x^m} < {x^n} \Rightarrow m < n \;
  $
We have other operational formulas for the powers with the same base: In multiplication the powers are added and in division they are subtracted. These are known as product and quotient rules respectively.
The given equation is pronounced as x raised to the power m is equal to x raised to the power n.