1. Splash Screen

2. Five-Minute Check (over Lesson 9–5) Then/Now
Key Concept: Power of a Power Property
Example 1: Find the Power of a Power
Key Concept: Power of a Product Property
Example 2: Find the Power of a Product
Example 3: Find the Power of a Product
Example 4: Real-World Example: Find the Power of a Product
Concept Summary: Powers
Lesson Menu

3. Write 2.003 × 104 in standard form.
B. 20,030 C
D. 203
5-Minute Check 1

4. Write 3.45 × 10–3 in standard form.
B. 345 C D
5-Minute Check 2

5. Write 169,000,000 in scientific notation.
B × 107
C × 108
D × 109
5-Minute Check 3

6. Write 0.004 in scientific notation.
B. 0.4 × 10–4
C. 4.0 × 103
D. 4.0 × 10–3
5-Minute Check 4

7. Which is correctly ordered from least to greatest?
B × 10–1, 6000, 9.8 × 103, 8.0 × 104
C × 10–1, 6000, 8.0 × 104, 9.8 × 103
D. 6000, 5.3 × 10–1, 9.8 × 103, 8.0 × 104
5-Minute Check 5

8. An amoeba is meter long. Which of the following represents this length in scientific notation?
A. 2.0 × 104 m
B. 0.2 × 103 m
C. 2.0 × 10–4 m
D. 0.2 × 10–3 m
5-Minute Check 6

9. You multiplied and divided monomials. (Lesson 9–3)
Find the power of a power.
Find the power of a product.
Then/Now

10. Concept A

11. A. Simplify (122)3. (122)3 = 122 ● 3 Power of a Power = 126 Simplify.
Find the Power of a Power
A. Simplify (122)3.
(122)3 = 122 ● 3 Power of a Power
= 126 Simplify.
Answer: 126
Example 1

12. B. Simplify (f 5)7. (f 5)7 = f 5 ● 7 Power of a Power = f 35 Simplify.
Find the Power of a Power
B. Simplify (f 5)7.
(f 5)7 = f 5 ● 7 Power of a Power
= f 35 Simplify.
Answer: f 35
Example 1

13. A. Simplify (96)4.
A. 964
B. 942
C. 910
D. 924
Example 1 CYP A

14. B. Simplify (m3)5.
A. m2
B. m8
C. m15
D. 3m5
Example 1 CYP B

15. Concept B

16. (2v 6)4 = 2 4● (v 6)4 Power of a Product
Find the Power of a Product
A. Simplify (2v6)4.
(2v 6)4 = 2 4● (v 6)4 Power of a Product
= 24 ● v6 ● 4 Power of a Power
= 16v24 Simplify.
Answer: 16v 24
Example 2

17. (–5a3b4)2 = (–5) 2 ● (a3)2 ● (b4)2 Power of a Product
Find the Power of a Product
B. Simplify (–5a3b4)2.
(–5a3b4)2 = (–5) 2 ● (a3)2 ● (b4)2 Power of a Product
= (–5)2 ● (a3 ● 2) ● (b4 ● 2) Power of a Power
= 25a6b8 Simplify.
Answer: 25a6b8
Example 2

18. A. Simplify (3m2)4.
A. 12m6
B. 12m8
C. 81m6
D. 81m8
Example 2 CYP A

19. B. Simplify (–3a4b5)2. A. –9a6b7 B. –9a8b10 C. 9a6b7 D. 9a8b10
Example 2 CYP B

20. GEOMETRY Find the area of a square with sides of length 9x3y5.
Find the Power of a Product
GEOMETRY Find the area of a square with sides of length 9x3y5.
A = s2 Formula for the area of a square
= (9x3y5)2 Replace s with 9x3y5.
= 92 ● (x3)2 ● (y5)2 Power of a Product
= 92 ● x3 ● 2 ● y5 ● 2 Power of a Power
= 81x6y10 Simplify.
Answer: 81x6y10
Example 3

21. Find the area of a square with sides of length 4x5y3.
A. 8x7y6
B. 8x10y6
C. 16x10y6
D. 16x7y6
Example 3

22. S = 4 ● 3.14 ● r 2 Write the equation.
Find the Power of a Product
BIOLOGY A spherical bacterium has a radius of 1.5 × 10–4 millimeters. Use the formula S = 4 ● 3.14 ● r 2 to find the surface area S of a sphere with a radius r. Express your answer in scientific notation.
S = 4 ● 3.14 ● r 2 Write the equation.
= 4 ● 3.14 ● (1.5 × 10–4)2 Replace r with 1.5 × 10–4.
= 4 ● 3.14 ● (1.5)2 ● (10–4)2 Power of a Product.
= 4 ● 3.14 ● 2.25 ● 10–8 Simplify.
= × 10–8 Multiply.
Example 4

23. = 2.826 × 10–7 Express the answer in scientific notation.
Find the Power of a Product
= × 10–7 Express the answer in scientific notation.
Answer: The surface area of the spherical bacterium is × 10–7 square millimeters.
Example 4

24. BIOLOGY A spherical bacterium has a radius of 5 × 10–5 millimeters
BIOLOGY A spherical bacterium has a radius of 5 × 10–5 millimeters. Use the formula S = 4 ● 3.14 ● r 2 to find the surface area of a sphere with radius r. Express the answer in scientific notation.
A × 10–5 mm2
B × 10–8 mm2
C. 314 × 10–10 mm2
D × 10–5 mm2
Example 4

25. Concept C

26. End of the Lesson