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# Exercise 3.1

7th Maths : Term 2 Unit 3 : Algebra : Exponents and Powers, Laws of Exponents: Exercise 3.1 : Fill in the blanks, Say true or false, Find the value of the following, Objective type questions, Text Book Back Exercises Questions with Answers, Solution

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) 11=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) 7x × 72

7x+2

(iv) 25 ÷ 23

25–3 = 22

(v)188 ÷ 184

188 – 4 = 184

(vi) ( 64 )3

64x3 = 612

(vii) ( xm )0

xmx° = x° = 1

(viii) 95 × 35

(9 × 3)5 = 275

(ix) 3y × 12y

(3×12)y = 36y

(x) 256 × 56

(25 × 5)6 = 1256

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

(i) a b + ba

32 + 23

[3 × 3] + [2 × 2 × 2 ]

9 + 8 = 17

(ii) a a bb

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 = 35x7 = 335

(iii) ( 52 × 58 ) ÷ 55 = (52+8) ÷ 55 = 510–5 = 55

(iv) 20 × 30 × 4= 1 × 1 × 1 = 1

(v)  [43 × a8 × b2 ] / [43×a5×b2]

= 45–3 × a8–5 × b3–2 = 42 × a3 × b = 4 × 4a3b = 16a3b

Objective type questions

12.  a × a × a × a × a is equal to

(i) a5

(ii) 5a

(iii) 5a

(iv) a + 5

13. The exponential form of 72 is

(i) 72

(ii) 27

(iii) 22 ×33

(iv) 23 × 32

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

(i) a

(ii) 13

(iii) 3

(iv) 10

15. How many zeros are there in 10010 ?

(i) 2

(ii) 3

(iii) 10

(iv) 20

16. 240 + 240 is equal to

(i) 440

(ii) 280

(iii) 241

(iv) 480

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) 7x+2 (iv) 22 (v) 184 (vi) 612 (vii) 1 (viii) 275 (ix) 36y (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

Tags : Algebra | Term 2 Chapter 3 | 7th Maths , 7th Maths : Term 2 Unit 3 : Algebra
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7th Maths : Term 2 Unit 3 : Algebra : Exercise 3.1 | Algebra | Term 2 Chapter 3 | 7th Maths