Question

A positive integer raised to an odd or an even positive power is always postive true or false​

Answer 1

Answer:

true

Step-by-step explanation:

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Answer 2

Answer:

true

Step-by-step explanation:

How do you prove that an odd positive integer raised to a positive power results in an odd number?

What is true is that an odd positive integer raised to a positive integer power results in an odd number. Without specifying that the exponent has to be integer too, you could come up with 3log32 : the base is an odd positive integer (3), the exponent is positive, but the result is 2 which is an even integer number (I know that was a little cherry-picked, but actually for a general positive exponent the result isn’t even an integer).

But if we require the exponent to be integer too, then the result is surely an odd integer number. You can prove it very easily by induction.

Let k be any odd positive integer. Then:

k1 is odd because it’s equal to k , which is odd by hypothesis;

if n is any positive integer, kn+1 is odd because it’s equal to kn⋅k , which is the product of two odd numbers ( kn is odd by inductive hypothesis).

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