Question

Say true or false and justify your answer:
\[{{3}^{0}}={{(1000)}^{0}}\]

Answer 1

Hint:
We are given a question in which we have to compare these two values. On seeing the exponential powers means we need to know the property of exponents which says when the exponential power of any variable/constant/function that is any non-zero quantity whose exponential power is zero is equal to unity or \[1\]. Its value is independent of the base of the exponents; whatever it is there in the base accepts zero; its value will always be equal to \[1\].

Complete step by step solution:
We are given, \[{{3}^{0}}\] and \[{{(1000)}^{0}}\],
 We have to compare them
Since we know that according to the exponential property that the exponential power of any nom-zero function/variable/constant is always equal to \[1\].
\[\Rightarrow {{x}^{0}}={{y}^{0}}={{1}^{0}}={{1000}^{0}}......\]
As in this question we have,
\[{{3}^{0}}\], here exponential power is zero means its value is \[1\]
Also, in \[{{(1000)}^{0}}\] , exponential power is zero means its value is \[1\]
Thus, these two are equal and have value equals to one.
Hence, the given statement is true.

Note:
It is noted that any number, expression and function raised to zero is always equal to one. It is always proved by the exponential series that is \[{{e}^{x}}=1+x+{}^{{{x}^{2}}}/{}_{2}....\] in this when we put \[x\] equal to zero \[(x=0)\] we get one. Hence just remember that we will prove this in higher secondary standard.