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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

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

Write 3.45 × 10–3 in standard form. B. 345 C. 0.0345 D. 0.00345 5-Minute Check 2

Write 169,000,000 in scientific notation. B. 16.9 × 107 C. 1.69 × 108 D. 0.169 × 109 5-Minute Check 3

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

Which is correctly ordered from least to greatest? B. 5.3 × 10–1, 6000, 9.8 × 103, 8.0 × 104 C. 5.3 × 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

An amoeba is 0.0002 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

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

Concept A

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

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

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

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

Concept B

(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

(–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

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

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

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

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

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. = 28.26 × 10–8 Multiply. Example 4

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

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. 31.4 × 10–5 mm2 B. 3.14 × 10–8 mm2 C. 314 × 10–10 mm2 D. 3.14 × 10–5 mm2 Example 4

Concept C

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