Question

Find \[{a^0} = 1\]. Is it true or false?
a) \[True\]
b) \[False\]

Answer 1

Hint: Here we are given to find that when any number is raised to the power zero, the value comes out to be \[1\] or not. To do this we take the left hand side of the given equation. Then, since we know that the subtraction of two same numbers comes out to be zero, we will replace zero with \[x - x\]. Then we will proceed to reach the required result.

 Formula used: Let \[a,b,c\] be any real number and \[a\] is not equal to zero, that is
\[a,b,c \in R\] and\[a \ne 0\], then we can say that,\[{a^{b - c}} = \dfrac{{{a^b}}}{{{a^c}}}\].

Complete step-by-step answer:
In the question given above, that is\[{a^0} = 1\], we take the LHS part of the equation. We know that \[0\] can be written as a subtraction of two same numbers. So we can write the LHS as
\[{a^0} = {a^{x - x}}\].
Now, we know that according to the property of exponentials, \[{a^{b - c}} = \dfrac{{{a^b}}}{{{a^c}}}\]. Using this property we can write the above step as written below.
\[
   \Rightarrow {a^0} = \dfrac{{{a^x}}}{{{a^x}}} \\
   \Rightarrow {a^0} = 1 \\
 \]
Thus we can get the result as a) \[True\].

So, the correct answer is “Option A”.

Note: This is not carefully noted here that this \[{a^0} = 1\] works only when the base part that is \[a\] is not equal to zero. Then it turns into an indeterminate form of\[{0^0}\]. Above value in the question is in the exponential form. The below written part \[a\] is called the base and the raised part is called the power of the base.