LAWS OF EXPONENTS
I. Product Of Powers
If the expressions multiplied have the same base, add the exponents.
[tex]x^{a} \: • \: x ^{b} = x^{a+b} [/tex]
II. Power Of A Power
If the expression raised to a number is raised by another number, multiply the exponents.
[tex](x^{a})^{b} = x^{ab}[/tex]
III. Power Of A Product
If the multiplied expressions is raised by a number, multiply exponents then multiply the expressions.
[tex](x^{a}x^{b})^{c} = x^{ac} \: x^{bc} \\ (xy)^{a} = x^{a} y^{a}[/tex]
IV. Quotient Of Power
If the ratio of two expressions is raised to a number, then
Case 1. [tex] \displaystyle \frac{x^{a}}{x^{b}} = \displaystyle x^{a+b}[/tex], where a > b.
Case 2. [tex] \displaystyle \frac{x^{a}}{x^{b}} = \displaystyle \frac{1}{x^{b-a}}[/tex], where a < b.
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