English | Español

Try our Free Online Math Solver!

Online Math Solver

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Non-negative Exponents

Overview

• Section 5.1 in the textbook:
– Review of exponential notation
– Using the Product Rule
– Using the Power Rule
– Further applications of the Power Rule
– Using the Quotient Rule
Expressions Raised to the 0 Power
Review of Exponential
Notation
Review of Exponential Notation

• Consider 34 What is its expanded form?
• Consider (-3)4 What is its expanded form?
• What about -34?
• What about (½)3?
• Recall an exponential expression is made
up of a base raised to a power
– xa = x · x · x · x · x · x · x · … · x (a times)
– Identifying the base is the key
Using the Product Rule
Product Rule

• Consider x4 · x5 How does this expand?
x·x·x·x · x·x·x·x·x
x9

Product Rule:
–When multiplying LIKE BASES (the same
variable ), add the exponents

– Only applies when the operation is
multiplication
Product Rule (Example)

Ex 1: Simplify:

Using the Power Rule
Power Rule

• Consider How does this expand ?

x8 (using the Product Rule)

• Power Rule:
–When raising variables to a power, multiply
the exponents
– Only applies when the exponent is outside a
set of parentheses
PRODUCT Rule versus POWER
Rule

• Be careful not to confuse:
Product Rule: ( multiplying LIKE
bases)
Power Rule: (exponent appears with
NO base)
– It is a common mistake to mix up the
Product Rule and the Power Rule!
Power Rule (Example)

Ex 2: Simplify:

Quotient Rule
Quotient Rule

• Consider How does this expand?
x·x·x·x·x / x·x
x3

• Quotient Rule:
–When dividing LIKE BASES (the same
variable), subtract the exponents
– Only applies when the operation is division
Quotient Rule (Example)

Ex 3: Simplify:

Expressions Raised to the 0
Power
Expressions Raised to the 0 Power

• Consider x0
– As long as x ≠ 0, x0 = 1
• Can see this by applying the quotient rule
– x can also be an expression
– Be aware of what the zero power is affecting

Expressions Raised to the 0
Power (Example)

Ex 4: Simplify:

Summary

• After studying these slides, you should know how to do
the following:
– Understand exponential notation
– Evaluate an exponential expression given a value
– Understand and use the product rule
– Understand and use the power rule
– Recognize both powers of products and powers of quotients
– Understand and use the quotient rule
– Understand the meaning of an expression raised to the zero
power
Additional Practice
– See the list of suggested problems for 5.1
• Next lesson
Negative Exponents and Scientific Notation (Section 5.2)
Prev Next