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

```Carpentry & Joinery
Phase 4
Module 1 Unit 13
Powers, Roots & Indices
Sample Questions & Solutions
Carpentry & Joinery
Phase 4
Module 1 Unit 13
Powers, Roots & Indices
• Use repeated multiplication to evaluate
the following: (a) 9², (b) 15², (c) 2⁴, (d)
8³, (e) 10³
(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
Carpentry & Joinery
Phase 4
Module 1 Unit 13
Powers, Roots & Indices
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Write the following as a single power:
(a) 5² x 5⁴
(b) 5³ x 5
(c) 7 x 7
(d) 8³ x 8³
(e) 4² x 4⁶
(f) 4³ x 4² x 4⁵
Carpentry & Joinery
Phase 4
Module 1 Unit 13
Powers, Roots & Indices
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(a) 5² x 5⁴ = 5⁶
(2 + 4 = 6)
(b) 5³ x 5 = 5⁴
(3 + 1 = 4)
(c) 7 x 7 = 7²
(1 + 1 = 2)
(d) 8³ x 8³ = 8⁶
(3 + 3 = 6)
(e) 4² x 4⁶ = 4⁸
(2 + 6 = 8)
(f) 4³ x 4² x 4⁵ = 4¹⁰ (3 + 2 + 5 = 10)
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
Carpentry & Joinery
Phase 4
Module 1 Unit 13
Powers, Roots & Indices
(a)6⁵ = 6² (5 – 3 = 2)
6³
(b)7⁶ = 7 (6 – 5 = 1)
7⁵
(c)8⁴ = 8² (4 – 2 = 2)
8²
(d)3⁵ = 3⁴ (5 – 1 = 4)
3
(e)4³ = 4² ( 3 – 1 = 2)
4
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
Carpentry & Joinery
Phase 4
Module 1 Unit 13
Powers, Roots & Indices
(a) (4³)² = 4⁶
(3 x 2 = 6)
(b) (5⁴)³ = 5¹² (4 x 3 = 12)
(c) (6²)⁴ = 6⁸
(2 x 4 = 8)
(d) (5¹´²)² = 5 ( ½ of 2 = 1)
(e) (8²´³)³ = 8² (⅔ of 3 = 2)
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
Carpentry & Joinery
Phase 4
Module 1 Unit 13
Powers, Roots & Indices
(a) 16¹´² = √16 = 4
(b) 36¹´² = √36 = 6
(c) 3 x 81¹´² = 3 x √81 = 3x 9 = 27
(d) 5(49)¹´² = 5 x √49 = 5 x 7 = 35
(e) 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:
2⁵ x 2³
2⁴
5² x 5⁴
5³
8² x 8⁵
8⁶
7² x 7⁴
7³
3⁷ x 3
3⁵
Carpentry & Joinery
Phase 4
Module 1 Unit 13
Powers, Roots & Indices