Question

Which of the following values are equal ?
I)\[1^{4}\]
II) \[4^{0}\]
III) \[0^{4}\]
IV) \[4^{1}\]
A. I and II
B. II and III
C. I and III
D. I and IV

Answer 1

Hint: In this question , we need to find which of the given expression values are equal. First let us know about the power. Mathematically , Power is nothing but raising a base number to the exponent. Then let us find the value of the given expression one by one . Then from the values, we can find which of the expressions are equal.

Complete step by step solution:
Now let us find the value of the given expression one by one .
First let us consider (I) \[1^{4}\]
On expanding,
We get,
\[\Rightarrow \ 1^{4} = 1 \times 1 \times 1 \times 1\]
On multiplying,
We get,
\[1^{4} = 1\]
Next (II) \[4^{0}\]
We know that any number to the power \[0\] is \[1\] .
Thus \[4^{0}\] is \[1\] .
Then \[0^{4}\]
On expanding,
We get
\[0^{4} = 0 \times 0 \times 0 \times 0\]
On multiplying,
We get,
\[0^{4} = 0\]
We also know that zero to the power any number is \[0\] .
Finally (IV) \[4^{1}\]
We know that \[4^{1} = 4\]
Now we can compare the values to find which are equal.
Now on observing the values of all the expression,
\[1^{4}\] is equal to \[4^{0}\]
Thus I and II are equal.
Final answer :
\[1^{4}\] is equal to \[4^{0}\] that is, I and II are equal.
Option A). I and II is the correct answer.

Therefore, the correct option is A

Note: In order to solve these types of questions, we should have a strong grip over powers and exponent. We should know the difference between the powers and the exponent. Power is nothing but raising a base number to the exponent whereas exponent is a small number which is positioned at the up-right of the base number. We should be careful while expanding our power.