Splash Screen. Lesson Menu Five-Minute Check (over Lesson 6–5) CCSS Then/Now Key Concept: Example 1:Radical and Exponential Forms Example 2:Evaluate Expressions.

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Presentation transcript:

Splash Screen

Lesson Menu 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 5-Minute Check 1 A. B. C. D.

Over Lesson 6–5 5-Minute Check 2 A. B. C. D.

Over Lesson 6–5 5-Minute Check 3 A. B. C. D.

Over Lesson 6–5 5-Minute Check 4 A. B. C. D.

Over Lesson 6–5 5-Minute Check 5 A. B. C. D.

Over Lesson 6–5 5-Minute Check 6 A. B. C. D.

CCSS Mathematical Practices 1 Make sense of problems and persevere in solving them.

Then/Now You used properties of exponents. Write expressions with rational exponents in radical form and vice versa. Simplify expressions in exponential or radical form.

Concept

Example 1 Radical and Exponential Forms Definition of A. Write in radical form. Answer:

Example 1 Radical and Exponential Forms Definition of Answer: B. Write in exponential form.

Example 1 A. Write in radical form. A. B. C. D.

Example 1 A. B. C. D. B. Write in exponential form.

Example 2 Evaluate Expressions with Rational Exponents A. Evaluate. Simplify. Method 1 Answer:

Example 2 Evaluate Expressions with Rational Exponents Method 2 Multiply exponents. Power of a Power Answer:

Example 2 Evaluate Expressions with Rational Exponents Method 1 Answer: 4 Power of a Power Factor. Expand the square. Find the fifth root. B. Evaluate.

Example 2 Evaluate Expressions with Rational Exponents Answer:4 Method 2 32 = 2 5 Power of a Power Multiply exponents. 2 2 = 4

Example 2 A. Evaluate. A. B. C. D.

Example 2 B. Evaluate. A. B. C. D.

Concept

Example 3 Solve Equations with Rational Exponents B = 168 Answer: The formula predicts that he can lift at most 472 kg. 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. Original formula According to the formula, what is the maximum that a weightlifter weighing 168 kilograms can lift?

Example 3 A.300 kg B.340 kg C.380 kg D.400 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?

Example 4 Simplify Expressions with Rational Exponents A. Simplify. Multiply powers. Add exponents.Answer:

Example 4 Simplify Expressions with Rational Exponents B. Simplify. Multiply by.

Example 4 Simplify Expressions with Rational Exponents Answer:

Example 4 A. Simplify. A. B. C. D.

Example 4 B. Simplify. A. B. C. D.

Example 5 Simplify Radical Expressions A. Simplify. Rational exponents Power of a Power 16 = 2 4

Example 5 Simplify Radical Expressions Quotient of Powers Simplify. Answer:

Example 5 Simplify Radical Expressions B. Simplify. Rational exponents 2 2 = 4 Power of a Power Multiply. Simplify. Answer:

Example 5 Simplify Radical Expressions Multiply. C. Simplify. is the conjugate of. Answer:

Example 5 A. Simplify. A. B. C. D.

Example 5 B. Simplify. A. B. C. D.

Example 5 C. Simplify. A. B. C. D.

Concept

End of the Lesson