Topic 3Exponents

Coefficients

coefficient: a number in front of a variable or variables Ex: 5x^3 Ex2: 100 n^2 m^6

Exponential Rules

1. You cannot add exponents when they are not like terms. Ex: x^2 + x^3

2. When multiplying exponents with the same bases, you can add up their exponents, while keeping the same base.

Ex: (x^2) (x^3) = x^2+3 = x^5

3. When dividing exponents with the same bases, you can subtract their exponents, while keeping the same base.

Ex: 2^3 ÷ 2^1 = 2^3-1 = 2^2 You can also write out the each individual exponent and cancel out as needed. The

remaining numbers will become your answer.

Exponential Rules con’t

4. When you have an exponent inside of parentheses with an exponent on the outside of the parentheses, keep the base and multiply the exponents together.

Ex: (x^2) ^3 = x^(2)(3) = x^6

5. When you have a negative exponent, put one over the opposite value of the exponent.

Ex: w^-3 = 1/w^3

6. NEVER LEAVE NEGATIVE EXPONENTS IN YOUR ANSWERS!

7. When you have more than one base (multiplied together) inside of parentheses and an exponent outside of the parentheses, distribute the exponent over to each of the bases.

Ex: (xy)^4 = x^4 y^4

Exponential Rules con’t

8. When you have more than one base inside of parentheses (either addition or subtraction) with an exponent outside the parentheses, expand the contents of the parentheses.

Ex: (x+y)^2 = (x+y) (x+y) = x^2 + xy + xy + y^2 = x^2 + 2xy + y^2

9. When you have a fraction inside of parentheses with an exponent outside of the parentheses, distribute the exponent to the numerator and the denominator.

Ex: (x/y)^5 = (x^5/y^5)