Section 8-1: Zero and Negative Exponents Objectives: (1) To understand that numbers in the real...
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Section 8-1: Zero and Negative Exponents Objectives: (1) To understand that numbers in the real number system are represented in a variety of equivalent forms (2) To add, subtract, multiply and divide exponential expressions
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Transcript of Section 8-1: Zero and Negative Exponents Objectives: (1) To understand that numbers in the real...
Section 8-1: Zero and Negative Exponents
Objectives: (1) To understand that numbers in the real number system are represented in a variety of
equivalent forms(2) To add, subtract, multiply and divide exponential
expressions
Properties
• Zero Exponent Property– For every nonzero number a, a0 = 1• Examples
– 50 = 1 (-2)0 = 1 (-1.02)0 = 1 (1/2)0 = 1
• Negative Exponent Property– For every nonzero number a and integer n,
a-n= • Examples
– 6-4 = (-8)-1 =
na
1
46
1
8
1
Converting Negative Exponents to Positive Exponents
• Step 1: Make every number with a negative exponent a fraction (easiest way to convert any number into a fraction is putting it over 1)
• Step 2: Move the number to the other side of the fraction bar and change the sign
• Step 3: If there are no numbers left on one side of the fraction bar, put a 1 to represent that there was a number there originally.
Examples of Converting Negative Exponents
• 4-3 • 1 _ 43
• 1 _____ 4 • 4 • 4• 1__ This is what we call 64 simplifying a power
Simplifying an Exponential Expression
Simplify the expression4yx-3
4yX3
• Use the definition of negative exponents
• Simplify
• We’re done!• Tada!
3
14
xy
Simplifying an Exponential Expression
Simplify the expression:1w-4
w4
• Move the w to the other side of the fraction bar
• You’re done! • Tada!
Evaluating Exponential Expressions
Evaulate:3m2t-2 for t = -3, m = 23m2
t2 3(2)2
(-3)2 3(4) 912 943
• 1st: Convert to positive exponents
• 2nd: Plug in values (put them in parenthesis)
• 3rd : Simplify
• You’re done
Real-World Problem Solving
• Population Growth:A biologist is studying green peach aphids (a bug). In
the lab, the population doubles every week. The expression 1000 • 2w models an initial population of 1000 insects after w weeks of growth.a. Evaluate the expression for w = 0. Then describe what
the value of the expression represents in the situation.b. Evaluate the expression for w = -3. Then describe what
the value of the expression represents in the situation.
Part A
1000 • 2w
1000 • 20
1000 • 11000
• Plug in 0 for w• Now evaluate
• What does 1000 represent?
• The initial number of aphids
Part B
1000 • 2w
1000 • 2-3
1000 •
1000 • 125
• Plug in -3 for w• Now evaluate
• What does 125 represent?
• The number of aphids 3 weeks ago
8
1
32
1
