Transcript Slide 1

Non-negative Exponents
MATH 018
Combined Algebra
S. Rook
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
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Review of Exponential
Notation
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Review of Exponential Notation
• Consider (-3)4 What is its expanded form?
• What about -34?
• 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
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Using the Product Rule
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Product Rule
• Consider x2 ∙ x4 How does this expand?
• Product Rule: xa ∙ xb = xa+b
– When multiplying LIKE BASES (the same
variable), add the exponents
– Only applies when the operation is
multiplication
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Product Rule (Example)
Ex 1: Simplify:
a) 4a5b3 · 6a7b
b) 3x2y2z9 · -x4z8
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Using the Power Rule
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Power Rule
• Consider (x2)4 How does this expand?
• Power Rule: (xa)b = xab
– When raising variables to a power, multiply
the exponents
– Only applies when the exponent is outside a
set of parentheses
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PRODUCT Rule versus POWER
Rule
• Be careful not to confuse:
– Product Rule: x4 · x7 (multiplying LIKE
bases)
– Power Rule: (x4)7 (exponent appears with
NO base)
– It is a common mistake to mix up the
Product Rule and the Power Rule!
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Power Rule (Example)
Ex 2: Simplify:
a) (-4x3)2
b) (x5y7)3
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Quotient Rule
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Quotient Rule
• Consider x5 / x2 How does this expand?
• Quotient Rule: xa / xb = xa-b
– When dividing LIKE BASES (the same
variable), subtract the exponents
– Only applies when the operation is division
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Quotient Rule (Example)
Ex 3: Simplify:
8 3
16
x
y
a)
5
20x y
7 5 11
a
bc
b)
ab5
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Expressions Raised to the 0
Power
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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:
• (5x)0 ?
• 5x0 ?
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Expressions Raised to the 0
Power (Example)
Ex 4: Simplify:
a) (9x4y8)0
b) 18r9s0
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Summary
• After studying these slides, you should know how to do
the following:
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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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