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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Sample Questions & Solutions

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Use repeated multiplication to evaluate the following: (a) 9², (b) 15², (c) 2 ⁴, (d) 8³, (e) 10³ Answers:Answers: (a)9 x 9 = 81 (b)15 x 15 = 225 (c)2 x 2 x 2 x 2 = 16 (d)8 x 8 x 8 = 512 (e)10 x 10 x 10 = 1,000

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Write the following as a single power: (a)5² x 5 ⁴ (b)5³ x 5 (c)7 x 7 (d)8³ x 8³ (e)4² x 4 ⁶ (f)4³ x 4² x 4 ⁵

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Answers:Answers: = 5 ⁶ (2 + 4 = 6)(a)5² x 5 ⁴ = 5 ⁶ (2 + 4 = 6) = 5 ⁴ (3 + 1 = 4)(b)5³ x 5 = 5 ⁴ (3 + 1 = 4) = 7² (1 + 1 = 2)(c)7 x 7 = 7² (1 + 1 = 2) = 8 ⁶ (3 + 3 = 6)(d)8³ x 8³ = 8 ⁶ (3 + 3 = 6) = 4 ⁸ (2 + 6 = 8)(e)4² x 4 ⁶ = 4 ⁸ (2 + 6 = 8) = 4¹ ⁰ ( = 10)(f)4³ x 4² x 4 ⁵ = 4¹ ⁰ ( = 10)

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Express the following as a single power: (a)6⁵ 6³ (b)7⁶ 7⁵ (c)8⁴ 8² (d)3⁵ 3 (e)4³ 4

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Answers: Answers: 6² (a)6⁵ = 6² (5 – 3 = 2) 6³ 7 (b)7⁶ = 7 (6 – 5 = 1) 7⁵ 8² (c)8⁴ = 8² (4 – 2 = 2) 8² 3⁴ (d)3⁵ = 3⁴ (5 – 1 = 4) 3 4² (e)4³ = 4² ( 3 – 1 = 2) 4

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Write the following as a single power: (a) (4³)² (b) (5⁴)³ (c) (6²)⁴ (d) (5¹´²)² (e) (8²´³)³

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Answers: Answers: 4⁶ (a) (4³)² = 4⁶ (3 x 2 = 6) 5¹² (b) (5⁴)³ = 5¹² (4 x 3 = 12) 6⁸ (c) (6²)⁴ = 6⁸ (2 x 4 = 8) 5 (d) (5¹´²)² = 5 ( ½ of 2 = 1) 8² (e) (8²´³)³ = 8² (⅔ of 3 = 2)

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Calculate the value of the following: (a) 16¹´² (b) 36¹´² (c) 3 x 81¹´² (d) 5(49)¹´² (e) 2(25)¹´²

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Answers: Answers: 4 (a) 16¹´² = √16 = 4 6 (b) 36¹´² = √36 = 6 27 (c) 3 x 81¹´² = 3 x √81 = 3x 9 = (d) 5(49)¹´² = 5 x √49 = 5 x 7 = (e) 2(25)¹´² = 2 x √25 = 2 x 5 = 10

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Simplify the following: 2 ⁵ x 2³ 2 ⁴ 5² x 5 ⁴ 5³ 8² x 8 ⁵ 8 ⁶ 7² x 7 ⁴ 7³ 3 ⁷ x 3 3 ⁵

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Carpentry & Joinery Phase 4 Module 1 Unit 13 Powers, Roots & Indices Answers: Answers: so 2 ⁴ = 16 2 ⁵ x 2³ = (5 + 3)- 4 = 8 – 4 = 4 so 2 ⁴ = 16 2 ⁴ so 5³ = 125 5² x 5 ⁴ = (2 + 4)- 3 = 6 – 3 = 3 so 5³ = 125 5³ so 8¹ = 8 8² x 8 ⁵ = (2 + 5)- 6 = 7 – 6 = 1 so 8¹ = 8 8 ⁶ so 7³ = 343 7² x 7 ⁴ = (2 + 4)- 3 = 6 – 3 = 3 so 7³ = 343 7³ so 3³ = 27 3 ⁷ x 3 = (7 + 1)- 5 = 8 – 5 = 3 so 3³ = 27 3 ⁵

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