Nonnegative 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 3^{4} What is its expanded form? • Consider (3)^{4} What is its expanded form? • What about 3^{4}? • What about (½)^{3}? • Recall an exponential expression is made up of a base raised to a power – x^{a} = x · x · x · x · x · x · x · … · x (a times) – Identifying the base is the key 
Using the Product Rule 
Product Rule • Consider x^{4} · x^{5} How does this expand? x·x·x·x · x·x·x·x·x x^{9 } • 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 ? x^{8} (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 x^{3} • 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 x^{0} 
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) 
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