Answer:
a. [tex]\sqrt{x^n}[/tex] = [tex]x^\frac{n}{2}[/tex]
b. [tex]\sqrt{x^n} = x^\frac{(n-1)}{2}\sqrt{x}[/tex]
Step-by-step explanation:
a) When n is even, then it is divisible by 2. Because of this, you can write:
- [tex]\sqrt{x^n} = (x^n)^\frac{1}{2}[/tex]
- [tex]\sqrt{x^n} = x^\frac{n}{2}[/tex]
b) When n is odd, then n - 1 is even. This would make it divisible by 2, and there would be a remainder of 1, so we can write:
- [tex]\sqrt{x^n} = (x^n^-^1^+^1) ^\frac{1}{2}[/tex]
- [tex]\sqrt{x^n} = (x^n^-^1[/tex] × [tex]x)^\frac{1}{2}[/tex]
- [tex]\sqrt{x^n} = x^\frac{(n-1)}{2}[/tex] × [tex]x^\frac{1}{2}[/tex]
- [tex]\sqrt{x^n} = x^\frac{(n-1)}{2}\sqrt{x}[/tex]
