Question

Find the value of ${\left( { - 1} \right)^{50}}$
A) -1
B) 50
C) -50
D) 1

Answer 1

Hint: If the base is a negative number, then there are two possibilities that the exponent is an even number or an odd number. For the first case, if the exponent of a negative number is an even number then the answer will be a positive number. And for the second case if the exponent of a negative number is an odd number then the answer will be a negative number.
If the base is a positive number, then no need to check for an even number or an odd number. The answer will always be a positive number.
Then find the value of the given question.

Complete step-by-step solution:
In the given question base is -1 and the exponent is 50.
Now, we can see that the base has a negative number.
Therefore, we have to check for exponent whether it is an even number or an odd number.
Here, the exponent is 50 that is an even number.
We already know that the even power of any negative number gives the answer in positive value.
Let us find the value of ${\left( { - 1} \right)^{50}}$.
Here, ${\left( { - 1} \right)^{50}}$means that (-1) is multiplied 50 times.
After multiplication,
$ \Rightarrow {\left( { - 1} \right)^{50}} = 1$
Therefore, we can say that when the exponent is even its sign is changed.

Option D is the correct answer.

Note: Let us take an example of the second case where the exponent of a negative number is an odd number.
Example: Find the value of ${\left( { - 1} \right)^{51}}$.
We can see that the base has a negative number.
And the exponent is an odd number.
So, the answer will be a negative number.
$ \Rightarrow {\left( { - 1} \right)^{51}} = - 1$
For positive base value:
Example: Find the value of ${8^2}$.
Here, 8 is called the base and 2 is called the exponent.
In this example, the small number ‘2’ says to use 8 two times in a multiplication.
$ \Rightarrow {8^2} = 8 \times 8$
After doing multiplication,
$ \Rightarrow {8^2} = 64$