burgerandcheese
Junior Member
- Joined
- Jul 2, 2018
- Messages
- 85
Hi. I was learning modulus functions when I came across this:
"If x is any real number, then |x²| ≡ |x|² ≡ x²."
I was wondering if we could generalise it even further to:
If x is any real number, then |xⁿ| ≡ |x|ⁿ ≡ xⁿ for even n.
I asked two of my math teachers and on a Facebook group but the responses were:
1. |xⁿ| ≡ |x|ⁿ ≡ xⁿ if x≥0 and (-x)ⁿ if x<0 for any n
2. Yes
3. No such thing
What is correct?
"If x is any real number, then |x²| ≡ |x|² ≡ x²."
I was wondering if we could generalise it even further to:
If x is any real number, then |xⁿ| ≡ |x|ⁿ ≡ xⁿ for even n.
I asked two of my math teachers and on a Facebook group but the responses were:
1. |xⁿ| ≡ |x|ⁿ ≡ xⁿ if x≥0 and (-x)ⁿ if x<0 for any n
2. Yes
3. No such thing
What is correct?