Product Rule

• Look at the right and see what happens when you multiply powers that have the same base

• When you expand 3² you have two 3s being multiplied and when you expand 3³ you have three 3s being multiplied.

• All together how many 3s are you multiplying?

Product Rule Short Cut?!!

When you multiply same base powers you keep the base and add the exponents.

x² * x⁷ = x²⁺⁷ = x⁹

What if we have a more than one variable or coefficients?

When you multiply same base powers you multiply the coefficients and combine like bases by adding the exponents.

(2y⁵x²)(6y^-3x⁷) = 2⋅6 y^5+(-3) x²⁺⁷ = 12y²x⁹

Quotient Rule

• When dividing powers that have the same base think of dividing as the inverse of multiplying, so what is the inverse of adding?

• When you expand x⁵ you have five Xs being multiplied in the numerator and when you expand x² you have two Xs being multiplied in the denominator.

• So what happens when you have the Xs in the numerator and Xs in the denominator? Yup! you cross out the matching pairs!

• Now what did you end up with?

Quotient Rule Short Cut?!!

When you divide same base powers you keep the base and subtract the exponents.

x⁷ / x² = x^7-2 = x⁵

What if we have coefficients?