 # 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)
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