Product & Quotient Rules of Exponents
Laws of Exponents
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
Simplify the following:a11⋅a2⋅a0
Simplify the following:x3⋅y2⋅x2
Simplify the following:x3⋅x⋅x−2
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 = x7-2 = x5
Simplify the following:x2x16
Simplify the following:x2y6x9y7
Simplify the following:x−4x7
Simplify the following:x8x3
How is your understanding of this topic?