Section 8.3 Dividing Monomials and Raising a Power to a Power

Section 8.3 Dividing Monomials and Raising a Power to a Power

Things to Remember

Dividing Monomials

In dividing monomials, there are two things that you must keep in mind. First, you divide your coefficients, which are the numbers that are written before the variables. As for the exponents (the powers), you would subtract them.

ex.   bases stay the same. subtract the exponents (9 – 3 = 6)

1000000 (count the number of zeros) There are six zeros, which means that your final answer is  .

Raising a power to a power

When you raise a power to a power, you are multiplying the two exponents together. For instance, a variable raised to the 5th power and then to the 2nd power would result in that variable raised to the 10th power. However, when you are raising a coefficient to an exponent, you would multiply the coefficient by the number of times represented as the exponent. So, y raised to the 7th power then raised to the 3rd power is the same as saying 7 *7 * 7 .

Exponential Functions

FORMULA FOR EXPONENTIAL FUNCTIONS

A represents the initial value

B represents the base

C represents the exponent

BASE                  PROPERTIES                    GRAPH

B > 1                    x and y increases                   curves up to the right of the y-axis

B = 1                    straight line                              no curve (linear)

0 < B < 1             x increases, y decreases    curves up to the left of the y-axis

 

First graph

y=1                   

x and y                   no change        x increases and y decreases

increases

*Remember: Any number that has a power of zero will always result as one.

 

reference: hmk 3/8/11, Breese, p7