imhimanshu wrote:

Hi Instructors,

Request you to please clarify the below doubt on the usage of the property

\(x^y\) = 1

If X is not equal to 0 and\(x > 1\); Will the value of y be always 0.

I mean, isnt it possible that y has some irrational value that makes \(x^y\) = 1

Example; \(2^(1/irrational value) = 1\). If not, what can we infer about the value of whole expression if \(x^(1/irrational value)\)

A number that can be expressed as a ratio of two numbers is rational. However, roots, \(\pi\), and endless non-repeating decimals are irrational numbers; they cannot be written in a ratio of two numbers. Moreover, an infinite amount of irrational numbers exist between integers. But, in no way, there is an infinite amount of irrational numbers that make integers, applying the logic that you used above.

I believe you are thinking as if rational and irrational numbers acted like odd and even numbers. Even though O + O = E or O + E = O, no such relationship exists between rational and irrational numbers.

I hope this helps.

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