Tính chất
1. x0 = 1 ; x1 = x
2. xn . xm = xn+m
3. xn : xm = xn-m (x # 0, n>=m)
4. (xn)m = xn.m
5. (x.y)n = xn . yn
6. \(\left(\frac{x}{y}\right)^n=\frac{x}{y^n}^n\left[\left(x:y\right)^n=x^n:y^n\right]\)
7. xn = yn => x=y
8. x2n = y2n => x=y hoặc x=-y
9. xn >= xm (x>1) => n>=m
xn >= xm (0<x<1) => n<=m
10. \(\text{x2n >= 0}^{2n}\ge0vớimọix\in R\)
11. x2n + m >= m
12. xn = xm => n=m
13. \(x^n\ge x^m=>\frac{1}{x^n}\le\frac{1}{x^m}\)
14. \(\frac{1}{x^n}=x^{-n}\)
15. \(\left(\frac{x}{y}\right)^{-n}=\left(\frac{y}{x}\right)^n\)
16. (-x)2n =x2n
17. \(\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}\left(a,b\in Z,b\ne0\right)\)
