Rules for Exponents

Many important rules must be applied when dealing with exponents.

• The most important rule is that when multiplying or dividing number with exponents, make sure they have the same base.                                                                                                           Ex: x^2 and x^6 can be multiplied, but not x^2 times z^4

Other important rules include:

1. When multiplying: add the exponents. Ex: x^2 times x^3= x^3+2 ,or x^5
2. When dividing: subtract the exponents. Ex: x^7/x^3= X^7-3, or x^4
3. When in parenthesis: multiply the exponents. Ex: (x^2)^3= x^2x3, or x^6
4. When exponent is negative: create a fraction with 1 as the numerator and the base to the positive version of the exponent to the denominator. Ex: x^-5 = 1/x^5
5. When the exponent equals 1: the final answer is the number of the base. Ex: 8^1=8
6. When the exponent equals zero: the answer is always one. Ex: 4^0=1

This picture clearly displays the rules I have explained.