## Chapter 13 Exponents and Powers Exercise 13.1

**Question 1: Find the value of:(a) 2⁶**

Answer:

Answer:

= 2 x 2 x 2 x 2 x 2 x 2

= 64

**(b) 9³Answer:**

= 9 x 9 x 9

= 729

**(c) 11²Answer:**

= 11 x 11

= 121

**(d) 5⁴Answer:**

= 5 x 5 x 5 x 5

= 625

**Question 2: Express the following in exponential form:(a) 6 x 6 x 6 x 6Answer:**= 6⁴

**(b) t x tAnswer:**= t²

**(c) b x b x b x bAnswer:**= b⁴

**(d) 5 x 5 x 7 x 7 x 7Answer:**= 5² x 7³

**(e) 2 x 2 x a x a**

Answer:

= 2² x a²

Answer:

**(f) a x a x a x c x c x c x c x d**

Answer:

= a³ x c⁴ x d¹

Answer:

**Question 3: Express each of the following numbers using exponential notation:**

(a) 512

Answer:

(a) 512

Answer:

**(ii) 343Answer:**

**(iii) 729**

Answer:

Answer:

**(iv) 3125**

Answer:

Answer:

**Question 4: Identify the greater number, wherever possible, in each of the following?(i) 4³ or 3⁴Answer: **4³ = 4 x 4 x 4

= 64

3⁴ = 3 x 3 x 3 x 3

= 81

64 < 81

Therefore, 3⁴ is greater.

**(ii) 5³ or 3⁵**

Answer:

5³ = 5 x 5 x 5

Answer:

= 125

3⁵ = 3 x 3 x 3 x 3 x 3

= 243

125 < 243

Therefore, 3⁵ is greater.

**2⁸ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2**

(iii) 2⁸ or 8²

Answer:

(iii) 2⁸ or 8²

Answer:

= 256

8² = 8 x 8

= 64

256 < 64

Therefore, 2⁸ is greater.

**100² = 100 x 100**

(iv) 100² or 2¹⁰⁰

Answer:

(iv) 100² or 2¹⁰⁰

Answer:

= 10000

2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 1024¹⁰

10000 < 1024¹⁰

Therefore, 2¹⁰⁰ is greater.

(v) 2

(v) 2

**¹⁰ or 10²**

Answer:

2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Answer:

= 1024

10² = 10 x 10

= 100

1024 < 100

Therefore, 2¹⁰ is greater.

Question 5: Express each of the following as product of powers of their prime factors:

(i) 648

Answer:

Question 5: Express each of the following as product of powers of their prime factors:

(i) 648

Answer:

(ii) 405

Answer:

(iii) 540

Answer:

(iii) 540

Answer:

(iv) 3,600

Answer:

(iv) 3,600

Answer:

**= 2 × 10 × 10 × 10**

Question 6: Simplify:

(i) 2 × 10³

Answer:

Question 6: Simplify:

(i) 2 × 10³

Answer:

= 2 × 1000

= 2000

(ii) 7² × 2

(ii) 7² × 2

**= 7 × 7 × 2 × 2**

**²**

Answer:= 49 × 4

= 196

**= 2 × 2 × 2 × 5**

(iii) 2³ × 5

Answer:

(iii) 2³ × 5

Answer:

= 8 × 5

= 40

**= 3 × 4 × 4 × 4 × 4**

(iv) 3 × 4⁴

Answer:

(iv) 3 × 4⁴

Answer:

= 3 × 256

= 768

**= 0 × 10 × 10**

(v) 0 × 10²

Answer:

(v) 0 × 10²

Answer:

= 0 × 100

= 0

**= 5 × 5 × 3 × 3 × 3**

(vi) 5² × 3³

Answer:

(vi) 5² × 3³

Answer:

= 25 × 27

= 675

**= 2 × 2 × 2 × 2 × 3 × 3**

(vii) 2⁴ × 3²

Answer:

(vii) 2⁴ × 3²

Answer:

= 16 × 9

= 144

**= 3 × 3 × 10 × 10 × 10 × 10**

(viii) 3² × 10⁴

Answer:

(viii) 3² × 10⁴

Answer:

= 9 × 10000

= 90000

**= -4 × -4 × -4**

Question 7: Simplify:

(i) (-4)³

Answer:

Question 7: Simplify:

(i) (-4)³

Answer:

= -64

**= -3 × -2 × -2 × -2**

(ii) (-3) × (-2)³

Answer:

(ii) (-3) × (-2)³

Answer:

= -3 × -8

= 24

**= -3 × -3 × -5 × -5**

(iii) (-3)² × (-5)²

Answer:

(iii) (-3)² × (-5)²

Answer:

= 9 × 25

= 225

**= -2 × -2 × -2 × -10 × -10 × -10**

(iv) (-2)³ × (-10)³

Answer:

(iv) (-2)³ × (-10)³

Answer:

= -8 × -1000

= 8000

**2.7 × 10¹² ____ 1.5 × 10⁸**

Question 8: Compare the following numbers:

(i) 2.7 × 10¹² ; 1.5 × 10⁸

Answer:

Question 8: Compare the following numbers:

(i) 2.7 × 10¹² ; 1.5 × 10⁸

Answer:

**Comparing the exponents of base 10.**

**2.7 × 10¹² > 1.5 × 10⁸**

(ii) 4 × 10¹⁴ ; 3 × 10¹⁷

Answer:

(ii) 4 × 10¹⁴ ; 3 × 10¹⁷

Answer:

4 × 10¹⁴ ____ 3 × 10¹⁷

Comparing the exponents of base 10.

4 × 10¹⁴ < 3 × 10¹⁷

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