[br][color=#0000ff]Let [math]\Large \textcolor{blue}{x\geq 0}[/math] [/color] [color=#0000ff]and [i]n[/i] positive integer. Fraction power[/color] [color=#0000ff][math]\Large \textcolor{blue}{x^{\frac{1}{n}}}[/math][/color] [color=#0000ff]means real number, for which[/color][br][br]  [math]\Large \textcolor{blue}{x^\frac{1}{n}\geq 0\;\;\; \text{ and }\;\; (x^\frac{1}{n})^n=x.}[/math] [br][br] [br] [br][color=#0000ff]Let [color=#0000ff][math]\large \textcolor{blue}{x\geq 0}[/math] and [i]n[/i] positive integer and [i]m[/i] integer. Fraction power [math] \large\textcolor{blue}{x^\frac{m}{n}}[/math] means real number, for which[/color][br][br]  [math]\Large\textcolor{blue}{x^\frac mn=(x^\frac 1 n )^m.}[/math]   [br] [br] [br][color=#000000]Fraction power can be used instead of roots in some cases. Nowadays, there may not be specific button for roots. Based on mathematical definition, fraction powers are defined only for positive numbers[/color][/color]. [br][br][br][color=#0000ff]Examples:[/color][br][br] 1. [math] \sqrt 4 = 2 = 4^\frac 12[/math][br] [br] 2. [math] \sqrt[3] 8 = 2 = 8^\frac 13[/math][br] [br] 3. [math] \sqrt[3] {-8} = -2[/math][br] [br] 4. [math] (-8)^\frac 13 \text{ not defined}[/math][br] [br] 5. [math] -8^\frac 13=-(8^\frac 13)=-2[/math][br] [br][br]