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Five-Minute Check (over Lesson 6–5)
CCSS
Then/Now
Key Concept:
Example 1: Radical and Exponential Forms
Example 2: Evaluate Expressions with Rational Exponents
Key Concept: Rational Exponents
Example 3: Real-World Example: Solve Equations with Rational Exponents
Example 4: Simplify Expressions with Rational Exponents
Example 5: Simplify Radical Expressions
Concept Summary: Expressions with Rational Exponents
Over Lesson 6–5
A.
B.
C.
D.
Over Lesson 6–5
A.
B.
C.
D.
Over Lesson 6–5
A.
B.
C.
D.
Over Lesson 6–5
A.
B.
C.
D.
Over Lesson 6–5
A.
B.
C.
D.
Over Lesson 6–5
A.
B.
C.
D.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
You used properties of exponents.
• Write expressions with rational exponents in radical form and vice versa.
• Simplify expressions in exponential or radical form.
Radical and Exponential Forms
Definition of
A. Write in radical form.
Answer:
Radical and Exponential Forms
Definition of
Answer:
B. Write in exponential form.
A. Write in radical form.
A.
B.
C.
D.
A.
B.
C.
D.
B. Write in exponential form.
Evaluate Expressions with Rational Exponents
A. Evaluate .
Simplify.
Method 1
Answer:
Evaluate Expressions with Rational Exponents
Method 2
Multiply exponents.
Power of a Power
Answer:
Evaluate Expressions with Rational Exponents
Method 1
Answer: 4
Power of a Power
Factor.
Expand the square.
Find the fifth root.
B. Evaluate .
Evaluate Expressions with Rational Exponents
Answer: 4
Method 2 32 = 25
Power of a Power
Multiply exponents.
22 = 4
A. Evaluate .
A.
B.
C.
D.
B. Evaluate .
A.
B.
C.
D.
Solve Equations with Rational Exponents
B = 168
Answer: The formula predicts that he can lift at most 472 kg.
WEIGHTLIFTING The formulacan be used to estimate the maximum total massthat a weightlifter of mass B kilograms can liftusing the snatch and the clean and jerk.
Original formula
According to the formula, what is the maximumthat a weightlifter weighing 168 kilograms can lift?
A. 300 kg
B. 340 kg
C. 380 kg
D. 400 kg
Use the formula where M isthe maximum total mass that a weightlifter ofmass B kilograms can lift. According to theformula, what is the maximum that a weightliftercan lift if he weighs 80 kilograms?
Simplify Expressions with Rational Exponents
A. Simplify .
Multiply powers.
Add exponents.
Answer:
Simplify Expressions with Rational Exponents
B. Simplify .
Multiply by .
Simplify Expressions with Rational Exponents
Answer:
A. Simplify .
A.
B.
C.
D.
B. Simplify .
A.
B.
C.
D.
Simplify Radical Expressions
A. Simplify .
Rational exponents
Power of a Power
16 = 24
Simplify Radical Expressions
Quotient of Powers
Simplify.
Answer:
Simplify Radical Expressions
B. Simplify .
Rational exponents
22 = 4
Power of a Power
Multiply.
Simplify.
Answer:
Simplify Radical Expressions
Multiply.
C. Simplify .
is the conjugate
of .
Answer:
A. Simplify .
A.
B.
C.
D.
B. Simplify .
A.
B.
C.
D.
C. Simplify .
A.
B.
C.
D.
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