2. Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept:Product of Powers Example 1:Multiply Powers Example 2:Multiply Powers Example 3:Multiply Powers Key Concept:Quotient of Powers Example 4:Divide Powers Example 5:Divide Powers Example 6:Real-World Example Example 7:Simplify Expressions Five-Minute Check

3. Main Idea/Vocabulary Simplify real number expressions by multiplying and dividing monomials. monomial

4. NGSSS MA.8.A.6.3 Simplify real number expressions using the laws of exponents. MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems.

5. Key Concept

6. Example 1 Multiply Powers Simplify 7 6 7. Express using exponents. 7 6 7 = 7 6 7 1 7 = 7 1 = 7 6 + 1 The common base is 7. = 7 7 Add the exponents.

7. Example 1 Check7 6 · 7 = (7 · 7 · 7  7 · 7 · 7) · 7 = 7 · 7 · 7  7 · 7 · 7 · 7 = 7 7 Multiply Powers Answer:7 7

8. Example 1 CYP A.8 4 B.8 5 C.8 6 D.8 8 Simplify 8 8 5. Express using exponents.

9. Example 2 Simplify r 4 r 6. Express using exponents. Multiply Powers r 4 r 6 = r 4 + 6 The common base is r. = r 10 Add the exponents. Answer:r 10

10. Example 2 CYP A.t 4.5 B.t 7 C.t 11 D.t 18 Simplify t 9 t 2. Express using exponents.

11. Example 3 Multiply Powers Simplify –7x 2 11x 4. Express using exponents. –7x 2 11x 4 = (–7 11)(x 2 x 4 ) Commutative and Associative Properties = (–77)(x 2 + 4 ) The common base is x. = –77x 6 Add the exponents. Answer:–77x 6

12. Example 3 CYP A.–8n 30 B.–8n 11 C.8n 30 D.8n Simplify 4n 6 (–2n 5 ). Express using exponents.

13. Key Concept 4

14. Example 4 Divide Powers = 6 12 – 2 The common base is 6. = 6 10 Simply. Answer:6 10 Simplify. Express using exponents.

15. Example 4 CYP A.8 2 B.8 5 C.8 15 D.8 –5 Simplify. Express using exponents.

16. Example 5 Divide Powers = a 14 – 8 The common base is a. = a 6 Simply. Answer:a 6 Simplify. Express using exponents.

17. Example 5 CYP A.h 4 B.h 14 C.h 15 D.h 20 Simplify. Express using exponents.

18. Example 6 MEASUREMENT One centimeter is equal to 10 millimeters, and one kilometer is equal to 10 6 millimeters. How many centimeters are in one kilometer? 10 = 10 1 = 10 6 – 1 or 10 5 Quotient of Powers Answer:There are 10 5 centimeters in one kilometer.

19. Example 6 CYP A.10 3 times greater B.10 4 times greater C.10 8 times greater D.10 12 times greater MEASUREMENT One metric ton is equal to 10 6 grams and one hectogram is equal to 10 2 grams. How many times greater is a metric ton than a hectogram?

20. Group by common base. = 2 1 5 2 9 1 Subtract the exponents. = 2 25 9 5 2 = 25 = 450 Simplify. Example 7 Simplify Expressions Simplify Answer:450

21. Example 7 CYP A.144 B.1,152 C.1,536 D.9,116 Simplify. Express using exponents.

22. A.4 24 B.4 11 C.4 5 D.4 –5 Simplify 4 8 4 3. Express using exponents. Five Minute Check 1

23. A.–6x 7 y 4 z 2 B.6x 6 y 4 z 2 C.6x 6 y 4 z D.6x 7 y 4 z 2 Simplify (–3x 6 yz 2 )(–2xy 3 ). Express using exponents. Five Minute Check 2

24. A.9 5 B.9 –19 C.9 19 D.9 84 Five Minute Check 3 Simplify. Express using exponents.

25. A.a 15 b 30 B.a 8 b 13 C.a 2 b 10 D.a 2 b 7 Five Minute Check 4 Simplify. Express using exponents.

26. A.1,953,125 B.6,875 C.555,555,555 D.390,625 The population of Bangkok was 5 5 in 1620. By 1990, it increased 5 4 times. What was Bangkok’s population in 1990? Five Minute Check 5