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
A. Write
in radical form.
Definition of
Answer:
Radical and Exponential Forms
B. Write
in exponential form.
Definition of
Answer:
A. Write
A.
B.
C.
D.
in radical form.
B. Write
A.
B.
C.
D.
in exponential form.
Evaluate Expressions with Rational Exponents
A. Evaluate
.
Method 1
Simplify.
Answer:
Evaluate Expressions with Rational Exponents
Method 2
Power of a Power
Multiply exponents.
Answer:
Evaluate Expressions with Rational Exponents
B. Evaluate
Method 1
.
Factor.
Power of a Power
Expand the square.
Find the fifth root.
Answer: 4
Evaluate Expressions with Rational Exponents
Method 2
32 = 25
Power of a Power
Multiply exponents.
22 = 4
Answer: 4
A. Evaluate
A.
B.
C.
D.
.
B. Evaluate
A.
B.
C.
D.
.
Solve Equations with Rational
Exponents
WEIGHTLIFTING The formula
can be used to estimate the maximum total mass
that a weightlifter of mass B kilograms can lift
using the snatch and the clean and jerk.
According to the formula, what is the maximum
that a weightlifter weighing 168 kilograms can
lift?
Original formula
B = 168
Answer: The formula predicts that he can lift at
most 472 kg.
Use the formula
where M is
the maximum total mass that a weightlifter of
mass B kilograms can lift. According to the
formula, what is the maximum that a weightlifter
can lift if he weighs 80 kilograms?
A. 300 kg
B. 340 kg
C. 380 kg
D. 400 kg
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
16 = 24
Power of a Power
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
C. Simplify
.
is the conjugate
of
Multiply.
Answer:
.
A. Simplify
A.
B.
C.
D.
.
B. Simplify
A.
B.
C.
D.
.
C. Simplify
A.
B.
C.
D.
.