These basic properties of integer exponents can simplify algebraic and numeric expressions.
1.
[tex]x^{m}.x^{n} = x^{m+n} \\ x^{m}.x^{-n} = x^{m-n}[/tex]
Examples:
x².x⁵ = x²⁺⁵ = x⁷
x⁸.x⁻⁵ = x⁸⁻⁵ = x³
2.
[tex]x^{-n} = \frac{1}{x^{n}} \\ or \\ x^{n} = \frac{1}{x^{-n}} [/tex]
Examples:
[tex]3^{-2} = \frac{1}{3^{2}} = \frac{1}{9} \\ \frac{2}{2^{-2}} =2^{1}.2^{2} = 2^{1+2}=2^{3}=8[/tex]
3.
[tex](x^{m})^{n} = x^{mn} [/tex]
Examples
(x⁴)³ = x⁴ˣ³ = x¹²
(4²)² = 4²ˣ² = 4⁴ = (2²)⁴ = 2⁸
[tex]( \frac{2}{3^{2}})^{2} = \frac{2^{2}}{(3^{2})^{2}} = \frac{2^{2}}{3^{4}} [/tex]
Using these basic rules makes it easier to simplify algebraic and numeric expressions.
