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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 Lesson Menu
A. B. C. D. 5-Minute Check 1
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Mathematical Practices 1 Make sense of problems and persevere in solving them. CCSS
You used properties of exponents. Write expressions with rational exponents in radical form and vice versa. Simplify expressions in exponential or radical form. Then/Now
Concept
A. Write in radical form. Definition of Answer: Radical and Exponential Forms A. Write in radical form. Definition of Answer: Example 1
A. Write in radical form. Definition of Answer: Radical and Exponential Forms A. Write in radical form. Definition of Answer: Example 1
B. Write in exponential form. Radical and Exponential Forms B. Write in exponential form. Definition of Answer: Example 1
B. Write in exponential form. Radical and Exponential Forms B. Write in exponential form. Definition of Answer: Example 1
A. Write in radical form. A. B. C. D. Example 1
A. Write in radical form. A. B. C. D. Example 1
B. Write in exponential form. C. D. Example 1
B. Write in exponential form. C. D. Example 1
A. Evaluate . Method 1 Simplify. Answer: Evaluate Expressions with Rational Exponents A. Evaluate . Method 1 Simplify. Answer: Example 2
A. Evaluate . Method 1 Simplify. Answer: Evaluate Expressions with Rational Exponents A. Evaluate . Method 1 Simplify. Answer: Example 2
Method 2 Power of a Power Multiply exponents. Answer: Evaluate Expressions with Rational Exponents Method 2 Power of a Power Multiply exponents. Answer: Example 2
Method 2 Power of a Power Multiply exponents. Answer: Evaluate Expressions with Rational Exponents Method 2 Power of a Power Multiply exponents. Answer: Example 2
B. Evaluate . Method 1 Factor. Power of a Power Expand the square. Evaluate Expressions with Rational Exponents B. Evaluate . Factor. Method 1 Power of a Power Expand the square. Find the fifth root. Answer: Example 2
B. Evaluate . Method 1 Factor. Power of a Power Expand the square. Evaluate Expressions with Rational Exponents B. Evaluate . Factor. Method 1 Power of a Power Expand the square. Find the fifth root. Answer: 4 Example 2
32 = 25 Method 2 Power of a Power Multiply exponents. 22 = 4 Answer: Evaluate Expressions with Rational Exponents 32 = 25 Method 2 Power of a Power Multiply exponents. 22 = 4 Answer: Example 2
32 = 25 Method 2 Power of a Power Multiply exponents. 22 = 4 Answer: 4 Evaluate Expressions with Rational Exponents 32 = 25 Method 2 Power of a Power Multiply exponents. 22 = 4 Answer: 4 Example 2
A. Evaluate . A. B. C. D. Example 2
A. Evaluate . A. B. C. D. Example 2
B. Evaluate . A. B. C. D. Example 2
B. Evaluate . A. B. C. D. Example 2
Concept
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: Example 3
Answer: The formula predicts that he can lift at most 472 kg. 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. Example 3
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 Example 3
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 Example 3
A. Simplify . Multiply powers. Add exponents. Answer: Simplify Expressions with Rational Exponents A. Simplify . Multiply powers. Add exponents. Answer: Example 4
A. Simplify . Multiply powers. Add exponents. Answer: 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
Simplify Expressions with Rational Exponents Answer: Example 4
A. Simplify . A. B. C. D. Example 4
A. Simplify . A. B. C. D. Example 4
B. Simplify . A. B. C. D. Example 4
B. Simplify . A. B. C. D. Example 4
A. Simplify . Rational exponents 16 = 24 Power of a Power Simplify Radical Expressions A. Simplify . Rational exponents 16 = 24 Power of a Power Example 5
Quotient of Powers Simplify. Answer: Simplify Radical Expressions Example 5
Quotient of Powers Simplify. Answer: Simplify Radical Expressions Example 5
B. Simplify . Rational exponents 22 = 4 Power of a Power Multiply. Simplify Radical Expressions B. Simplify . Rational exponents 22 = 4 Power of a Power Multiply. Simplify. Answer: Example 5
B. Simplify . Rational exponents 22 = 4 Power of a Power Multiply. Simplify Radical Expressions B. Simplify . Rational exponents 22 = 4 Power of a Power Multiply. Simplify. Answer: Example 5
C. Simplify . is the conjugate of . Multiply. Answer: Simplify Radical Expressions C. Simplify . is the conjugate of . Multiply. Answer: Example 5
C. Simplify . is the conjugate of . Multiply. Answer: Simplify Radical Expressions C. Simplify . is the conjugate of . Multiply. Answer: Example 5
A. Simplify . A. B. C. D. Example 5
A. Simplify . A. B. C. D. Example 5
B. Simplify . A. B. C. D. Example 5
B. Simplify . A. B. C. D. Example 5
C. Simplify . A. B. C. D. Example 5
C. Simplify . A. B. C. D. Example 5
Concept
End of the Lesson