Question

If I have any terminating decimal, and raise it to the power of the denominator, will the result also be a terminating decimal?

Similarly if I have a recurring decimal, will it also be a recurring decimal?

Answer 1

in the first...i know the answer is yes..because any fixed number raised to a fixed number will result to a fixed number...

Answer 2

Yup.
If you think about it, use an example.
1/2. One half, squared, is a fourth. Both are terminating.

Answer 3

So what about non-terminating decimals

Answer 4

What about non-terminating decimals?

Answer 5

If you raise them to any integer power, will they still be terminating?

Answer 6

Oh, I see what you mean. Nope, for example:
1/7, raised to the seventh power, is not terminating.
At least, I'm pretty sure its not. =P

Answer 7

So if you had a non terminating fraction p/q
if you had (p/q)^q would that be non-terminating

Answer 8

Yup

Answer 9

Sure thanks