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

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Over Lesson 6–5

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B.

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Over Lesson 6–5

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B.

C.

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Over Lesson 6–5

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B.

C.

D.

Over Lesson 6–5

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B.

C.

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Over Lesson 6–5

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B.

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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.

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B.

C.

D.

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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 .

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B.

C.

D.

B. Evaluate .

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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 .

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B.

C.

D.

B. Simplify .

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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 .

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B.

C.

D.

B. Simplify .

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B.

C.

D.

C. Simplify .

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B.

C.

D.