Powers, Roots & Indices

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Powers, Roots & Indices. Sample Questions & Solutions. Powers, Roots & Indices. Use repeated multiplication to evaluate the following: (a) 9², (b) 15², (c) 2 ⁴ , (d) 8³, (e) 10³ 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 - PowerPoint PPT Presentation

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Powers, Roots & IndicesPowers, Roots & Indices
Sample Questions & Solutions
Powers, Roots & Indices
Use repeated multiplication to evaluate the following: (a) 9², (b) 15², (c) 2, (d) 8³, (e) 10³
Answers:
(c) 2 x 2 x 2 x 2 = 16
(d) 8 x 8 x 8 = 512
(e) 10 x 10 x 10 = 1,000
Carpentry & Joinery Phase 4 Module 1 Unit 13
Powers, Roots & Indices
(a) 5² x 5
(b) 5³ x 5
(c) 7 x 7
(f) 4³ x 4² x 4
Carpentry & Joinery Phase 4 Module 1 Unit 13
Powers, Roots & Indices
Answers:
(a) 5² x 5 = 5 (2 + 4 = 6)
(b) 5³ x 5 = 5 (3 + 1 = 4)
(c) 7 x 7 = 7² (1 + 1 = 2)
(d) 8³ x 8³ = 8 (3 + 3 = 6)
(e) 4² x 4 = 4 (2 + 6 = 8)
(f) 4³ x 4² x 4 = 4¹ (3 + 2 + 5 = 10)
Carpentry & Joinery Phase 4 Module 1 Unit 13
Powers, Roots & Indices
6 6³
7 7
8 8²
Powers, Roots & Indices
7 = 7 (6 – 5 = 1) 7
8 = 8² (4 – 2 = 2) 8²
3 = 3 (5 – 1 = 4) 3
4³ = 4² ( 3 – 1 = 2) 4
Carpentry & Joinery Phase 4 Module 1 Unit 13
Powers, Roots & Indices
(4³)²
(5)³
(6²)
(5¹´²)²
(8²´³)³
Powers, Roots & Indices
(5¹´²)² = 5 ( ½ of 2 = 1)
(8²´³)³ = 8² ( of 3 = 2)
Carpentry & Joinery Phase 4 Module 1 Unit 13
Powers, Roots & Indices
16¹´²
36¹´²
Powers, Roots & Indices
3 x 81¹´² = 3 x √81 = 3x 9 = 27
5(49)¹´² = 5 x √49 = 5 x 7 = 35
2(25)¹´² = 2 x √25 = 2 x 5 = 10
Carpentry & Joinery Phase 4 Module 1 Unit 13
Powers, Roots & Indices
Simplify the following:
2

8

Powers, Roots & Indices
Answers:
2 x 2³ = (5 + 3)- 4 = 8 – 4 = 4 so 2 = 16
2
5² x 5 = (2 + 4)- 3 = 6 – 3 = 3 so 5³ = 125

8² x 8 = (2 + 5)- 6 = 7 – 6 = 1 so 8¹ = 8
8
7² x 7 = (2 + 4)- 3 = 6 – 3 = 3 so 7³ = 343

3 x 3 = (7 + 1)- 5 = 8 – 5 = 3 so 3³ = 27
3