Download Number 6 - Exponent Laws Review

Math 10C
Real Numbers: Lesson #6
Exponents
Objective: By the end of this lesson, you will be able to:
Recall:
Exponents are used as a short way to write repeated multiplication:
e.g. 1) 35 means ________________________ = _______
In general, a n =
Terminology:
an
Multiplication Law:
When multiplying powers with like bases, ______________ the exponents.
e.g. 7 5  7 3 
Division Law:
When dividing powers with like bases, __________________ the exponents.
e.g.
x9
or x 9  x 3 
3
x
Power Law:
When taking the power of a power, _________________ the exponents.
 
e.g. 112
6

Power of a Product Law:
Apply the power law to ______________________ inside the brackets.
 
3
e.g. 2n5 
Power of a Quotient:
Apply the power law to both the ___________________ and the ___________________.
2
 13 
e.g.   
8
Zero Exponent:
Anything to the power of 0 equals _____. e.g. a 0 
Why? It is actually a special case of the division law:
Math 10C
Real Numbers: Lesson #6
e.g. 2) Use the exponent laws to write each as a single power, then evaluate:
4
510
a) 8
b) 2 3
5
 
c)
 32  35
 37
n
d)  
7
3
e.g. 3) Use the exponent laws to simplify each expression:
24n5m8
a) x 6  x 3
b)
6n 3m

c) 2ab

5 3
 36 x 6 y 5 

d) 
6 3 
 24 x y 
4
When working with exponent laws, it is very important to pay attention to the brackets –
especially with negative bases.
e.g. 4) What is the difference between 3r 4 , (3r)4 and (3r)4 ?
e.g. 5) Do the powers 7 0 and (7)0 equal the same thing? Why or why not?
Assignment:
Handout: Exponent Laws Review