Exercise 3.1

Exercise 3.1

1. Fill in the blanks.

(i) The exponential form 14⁹ should be read as 14 power 9.

(ii) The expanded form of p³ q² is p × p × p × q × q.

(iii) When base is 12 and exponent is 17, its exponential form is 12¹⁷.

(iv) The value of (14 × 21)⁰ is 1.

2. Say True or False.

(i) 2³ ×3² = 6⁵ False

(ii) 2⁹ × 3² = (2 × 3)^9×2 False

(iii) 3⁴×3⁷=3¹¹ True

(iv) 2⁰ = (1000)⁰ True

(v) 2³<3² True

3. Find the value of the following.

 (i) 2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64

 (ii) 11² =11 × 11 = 121

 (iii) 5⁴ = 5 × 5 × 5 × 5 = 625

 (iv) 9³ = 9 × 9 × 9 = 729

4. Express the following in exponential form.

 (i) 6 × 6 × 6 × 6 = 6⁴

(ii) t × t = t²

(iii) 5 × 5 × 7 × 7 × 7 = 5² × 7³

(iv) 2 × 2 × a × a = 2² × a²

5. Express each of the following numbers using exponential form.

(i) 512

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁹

(ii) 343

343 = 7 × 7 × 7 = 7³

(iii) 729

729 = 3 × 3 × 3 × 3 × 3 × 3 = 3⁶

(iv) 3125

3125 = 5 × 5 × 5 × 5 × 5 = 5⁵

6. Identify the greater number in each of the following.

 (i) 6³ or 3⁶

6³ = 6 × 6 × 6 = 216

3⁶ = 3 × 3 × 3 × 3 × 3 × 3 = 729

729 > 216

So, The greater number is 3⁶.

 (ii) 5³ or 3⁵

5³ = 5 × 5 × 5 = 125

3⁵ = 3 × 3 × 3 × 3 × 3 = 243

243 > 125

So, The greater number is 3⁵.

 (iii) 2⁸ or 8²

2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

8² = 8 × 8 = 64

256 > 64

So, The greater number is 2⁸

7. Simplify the following.

 (i) 7² × 3⁴

7 × 7 × 3 × 3 × 3 × 3

 49 × 81 = 3969

(ii) 3² × 2⁴

3 × 3 × 2 × 2 × 2 × 2

 9 × 16 = 144

(iii) 5² × 10⁴

5 × 5 × 10 × 10 × 10 × 10

25 × 10000 = 250000

8. Find the value of the following.

 (i) ( −4)²

(–4) × (–4) = l6

 (ii) (–3)×(–2)³

(–3) × (–2) × (–2) × (–2)

6 × 4 = 24

 (iii) ( −2)³ × ( −10)³

(–2) × (–2) × (–2) × (–10) × (–10) × (–10)

–8 × –1000 = 8000

9. Simplify using laws of exponents.

 (i) 3⁵ × 3⁸

3⁵⁺⁸ = 3¹³

 (ii) a ⁴ × a¹⁰

a⁴⁺¹⁰ = a¹⁴

(iii) 7^x × 7²

7^x+2

(iv) 2⁵ ÷ 2³

2^5–3 = 2²

(v)18⁸ ÷ 18⁴

18^{8 – 4} = 18⁴

(vi) ( 6⁴ )³

6^4x3 = 6¹²

(vii) ( x^m )⁰

x^mx° = x° = 1

(viii) 9⁵ × 3⁵

(9 × 3)⁵ = 27⁵

 (ix) 3^y × 12^y

(3×12)^y = 36^y

(x) 25⁶ × 5⁶

(25 × 5)⁶ = 125⁶

10. If a = 3 and b = 2 , then find the value of the following.

(i) a ^b + b^a

3² + 2³

[3 × 3] + [2 × 2 × 2 ]

9 + 8 = 17 

(ii) a ^a − b^b

 3³ – 2²

[3 × 3 × 3] – [2 × 2]

27 – 4 = 23

(iii) ( a + b)^b

(3 + 2)² = 5²

5 × 5 = 25

(iv) ( a − b)^a

(3 – 2)³ = 1³ = 1

11. Simplify and express each of the following in exponential form:

(i) 4⁵× 4²× 4⁴ = 4⁵⁺²⁺⁴ = 4¹¹

(ii) ( 3² × 3³ )⁷ = (3²⁺³)⁷ = 3^5x7 = 3³⁵

(iii) ( 5² × 5⁸ ) ÷ 5⁵ = (5²⁺⁸) ÷ 5⁵ = 5^10–5 = 5⁵

(iv) 2⁰ × 3⁰ × 4⁰ = 1 × 1 × 1 = 1

(v)  [4³ × a⁸ × b² ] / [4³×a⁵×b²]

= 4^{5–3 ×} a^8–5 × b^3–2 = 4² × a³ × b = 4 × 4a³b = 16a³b

Objective type questions

12.  a × a × a × a × a is equal to

(i) a⁵

(ii) 5^a

(iii) 5a

(iv) a + 5

Answer: (i) a⁵

13. The exponential form of 72 is

(i) 7²

(ii) 2⁷

(iii) 2² ×3³

(iv) 2³ × 3²

Answer: (iv) 2³ × 3²

14. The value of x in the equation a¹³ = x³ × a¹⁰ is

(i) a

(ii) 13

(iii) 3

(iv) 10

Answer: (i) a

15. How many zeros are there in 100¹⁰ ?

(i) 2

(ii) 3

(iii) 10

(iv) 20

Answer: (iv) 20

16. 2⁴⁰ + 2⁴⁰ is equal to

(i) 4⁴⁰

 (ii) 2⁸⁰

(iii) 2⁴¹

(iv) 4⁸⁰

Answer: (iii) 2⁴¹

ANSWERS:

Exercise 3.1

1. (i) 14 power 9 (ii) p × p × p × q × q (iii) 12¹⁷  (iv) 1

2. (i) false (ii) false (iii) true (iv) true (v) true

3. (i) 64 (ii) 121 (iii) 625 (iv) 729

4. (i) 6⁴ (ii) t² (iii) 5² × 7³ (iv) 2² × a²

5. (i) 2⁹ (ii) 7³ (iii) 3⁶ (iv) 5⁵

6. (i) 6³ (ii) 3⁵ (iii) 2⁸

7. (i) 3969 (ii) 144 (iii) 250000

8. (i) 16 (ii) 24 (iii) 8000

9. (i) 3¹³ (ii) a¹⁴ (iii) 7^x+2 (iv) 2² (v) 18⁴ (vi) 6¹² (vii) 1 (viii) 27⁵ (ix) 36^y (x) 125⁶

10. (i) 17 (ii) 23 (iii) 25 (iv) 1

11. (i) 4¹¹ (ii) 3³⁵ (iii) 5⁵ (iv) 1 (v) 16a³b

 Objective type questions

12. (i) a⁵

13. (iv) 2³ × 3²

14. (i) a

15. (iv) 20

16. (iii) 2⁴¹