Post on 22-Feb-2016
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Chapter 5 Section 7Rational Exponents
Objectives:•To write expressions with rational exponents in radical form and vice versa.•To simplify expressions in exponential or radical form
Warm-up: Type 1 writing3 lines or more – 2 minutes
Write two expressions with radicals, one that is simplified and one that is not. Explain the
difference between the two.”
30 seconds
Finish your thought.
Warm-up: Type 1 writing3 lines or more – 2 minutes
Write two expressions with radicals, one that is simplified and one that is not. Explain the difference between the two.”
Times up!
Put your pencils down.
1
except for when b is negative
and n is even
nnb b
except for when b is negative and n is even
mn mnb b
Example 1 Radical FormExample 2 Exponential FormExample 3 Evaluate Expressions with
Rational ExponentsExample 4
Rational Exponent with Numerator Other Than 1
Example 5 Simplify Expressions with Rational Exponents
Example 6 Simplify Radical Expressions
Write in radical form.
Answer: Definition of
Write in radical form.
Answer: Definition of
Write each expression in radical form.
a.
b.
Answer:
Answer:
Write using rational exponents.
Definition of Answer:
Write using rational exponents.
Definition of Answer:
Write each radical using rational exponents.
a.
b.
Answer:
Answer:
Evaluate
Method 1
Answer: Simplify.
Multiply exponents.
Method 2
Answer:
Power of a Power
Answer: The root is 4.
Evaluate .
Method 1 Factor.
Power of a Power
Expand the square.
Find the fifth root.
Answer: The root is 4.
Power of a Power
Multiply exponents.
Method 2
Evaluate each expression.
a.
b.
Answer: 8
Answer:
According to the formula, what is the maximum that U.S. Weightlifter Oscar Chaplin III can lift if he weighs 77 kilograms?
Answer: The formula predicts that he can lift at most 372 kg.
Weight Lifting The formula can be used to estimate the maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and the clean and jerk, combined.
Original formula
Use a calculator.
Oscar Chaplin’s total in the 2000 Olympics was 355 kg. Compare this to the value predicted by the formula.
Answer: The formula prediction is somewhat higher than his actual total.
Weight Lifting The formula can be used to estimate the maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and the clean and jerk, combined.
Answer: 380 kg
Answer: The formula prediction is slightly higher than hisactual total.
Weight Lifting Use the formula where M is the maximum total mass that a weight lifter of mass B kilograms can lift.
a. According to the formula, what is the maximum that a weight lifter can lift if he weighs 80 kilograms?
b. If he actually lifted 379 kg, compare this to the valuepredicted by the formula.
Practice – Adding/Multiplying Fractions
5 31.8 16
1 2 3 4 57.2 3 4 5 6
3 56.4 6
9 35.5 4
5 14.3 8
2 23.7 3
11 12.12 3
1 68.3 7
Simplifying Rational Exponents
• Has no negative exponents• Has no fractional exponents in the
denominator• Is not a complex fraction• The index is the smallest number possible
Simplify .
Multiply powers.
Answer: Add exponents.
Simplify .
Multiply by
Answer:
Simplify each expression.
a.
b.
Answer:
Answer:
Simplify .
Rational exponents
Power of a Power
Quotient of Powers
Answer: Simplify.
Simplify .
Rational exponents
Power of a Power
Answer: Simplify.
Multiply.
Answer: Multiply.
Simplify .
is the conjugate
of
Answer: 1
Simplify each expression.
a.
b.
c. Answer:
Answer: