Lesson 7-B Notes(7-2)
Dividing Monomials
TNSS A-SSE. B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity
represented by the expression.
TNSS A-APR.A.1 Understand that polynomials B.3 form a system analogous to the integers, namely, they are closed under the operations of
addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Past Target
I multiplied monomials.
Present Target
I can find the quotient of two
monomials.
Future Target
I will find quotients of numbers
expressed in scientific notation.
I can simplify expressions
containing negative and zero
exponents.
Quotient of Powers: to divide two powers that have the same base, ______________________________
the exponents
Ex 1: Simplify. Assume that no denominator equals 0.
a.
r13
r5
b.
x 7 y12
x 6 y3
Power of a Quotient: to find the power of a quotient, find the power of the
__________________________________ and the power of the __________________________________
Ex. 2: Simplify. Assume that no denominator equals 0.
æaö
a. ç ÷
èbø
4
æ 4c3d 2 ö
b. ç
4 ÷
è 5e ø
3
Zero Exponent Property: any nonzero number raised to the zero power is ___________
Ex 3: Simplify. Assume that no denominator equals 0.
æ 12m8n 7 ö
b. ç
5 10 ÷
è 8m n ø
0
a. 8
d.
0
25
e.
25
c.
𝑥𝑦 3
f.
𝑥𝑦 3
Negative Exponent Property: for any nonzero number a and any integer n , a-n =
𝑥8
𝑥8
a 5 b 3c 8
ab3c 5
1
1
and -n = a n
n
a
a
Ex. 4 – Complete the following pattern…
25
Simplified:
24
23
22
_____ ____ _____ _____
21
20
2−1
2−2
2−3
2−4
2−5
_____
_____
_____
_____
_____
_____
_____
Ex 5: Simplify. Assume that no denominator equals 0.
a. 7-3
c.
x -4 y 9
z -6
b.
1
c -5
10a 2 b-7c10
-3 2 -3
d. 25a b c
CHALLENGE---Simplify each expression.
a.
27a 4 b 6 c 9
9a3b 6 c15d -8
b.
(m-1n 2 )4
(m 2 n 4 )2