# 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

5³

8

7³

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

5³

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

7³

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

3

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

5³

8

7³

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

5³

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

7³

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

3

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