# NCERT Solutions for Class 7 Maths Chapter 13

## Exponents and Powers Class 7

### Exercise 13.1 : Solutions of Questions on Page Number : 252

Q1 :

Find the value of:

(i) 26 (ii) 93

(iii) 112 (iv)54

(i) 26 = 2 x 2 x 2 x 2 x 2 x 2 = 64

(ii) 93 = 9 x 9 x 9 = 729

(iii) 112 = 11 x 11 = 121

(iv)54 = 5 x 5 x 5 x 5 = 625

Q2 :

Express the following in exponential form:

(i) 6 x 6 x 6 x 6 (ii) t x t

(iii) b x b x b x b (iv) 5 x 5 x 7 x 7 x 7

(v) 2 x 2 x a x a (vi) a x a x a x c x c x c x c x d

(i) 6 x 6 x 6 x 6 = 64

(ii) t x t= t2

(iii) b x b x b x b = b4

(iv) 5 x 5 x 7 x 7 x 7 = 52 x 73

(v) 2 x 2 x a x a = 22 x a2

(vi) a x a x a x c x c x c x c x d = a3 c4 d

Q3 :

Express the following numbers using exponential notation:

(i) 512 (ii) 343

(iii) 729 (iv) 3125

Q4 :

Identify the greater number, wherever possible, in each of the following?

(i) 43 or 34 (ii) 53 or 35

(iii) 28 or 82 (iv) 1002 or 2100

(v) 210 or 102

Q5 :

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

(i) 648 (ii) 405

(iii) 540 (iv) 3,600

Q6 :

Simplify:

(i) 2 x 103 (ii) 72 x 22

(iii) 23 x 5 (iv) 3 x 44

(v) 0 x 102 ­­­­­ (vi) 52 x 33

(vii) 24 x 32 (viii) 32 x 104

Q7 :

Simplify:

(i) (- 4)3 (ii) (- 3) x (- 2)3

(iii) (- 3)2 x (- 5)2 (iv)(- 2)3 x (-10)3

Q8 :

Compare the following numbers:

(i) 2.7 x 1012; 1.5 x 108

(ii) 4 x 1014; 3 x 1017

### Exercise 13.2 : Solutions of Questions on Page Number : 260

Q1 :

Using laws of exponents, simplify and write the answer in exponential form:

(i) 32 × 34 × 38 (ii) 615 ÃƒÂ· 610 (iii) a3 × a2

(iv) 7x× 72 (v) (vi) 25 × 55

(vii) a4 × b4 (viii) (34)3

(ix) (x) 8t ÃƒÂ· 82

Q2 :

Simplify and express each of the following in exponential form:

(i) (ii) (iii)

(iv) (v) (vi) 20 + 30 + 40

(vii) 20 × 30 × 40 (viii) (30 + 20) × 50 (ix)

(x) (xi) (xii)

Q3 :

(i) 10 x 1011 = 10011 (ii) 23 > 52

(iii) 23 x 32 = 65 (iv) 30 = (1000)0

Q4 :

Express each of the following as a product of prime factors only in exponential form:

(i) 108 x 192 (ii) 270

(iii) 729 x 64 (iv) 768

Q5 :

Simplify:

(i) (ii) (iii)

### Exercise 13.3 : Solutions of Questions on Page Number : 263

Q1 :

Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

Q2 :

Find the number from each of the following expanded forms:

(a) 8 x 104 + 6 x 103 + 0 x 102 + 4 x 101 + 5 x 100

(b) 4 x 105 + 5 x 103 + 3 x 102 + 2 x 100

(c) 3 x 104 + 7 x 102 + 5 x 100

(d) 9 x 105 + 2 x 102 + 3 x 101

Q3 :

Express the following numbers in standard form:

(i) 5, 00, 00, 000 (ii) 70, 00, 000

(iii) 3, 18, 65, 00, 000 (iv) 3, 90, 878

(v) 39087.8 (vi) 3908.78

Q4 :

Express the number appearing in the following statements in standard form.

(a) The distance between Earth and Moon is 384, 000, 000 m.

(b) Speed of light in vacuum is 300, 000, 000 m/s.

(c) Diameter of the Earth is 1, 27, 56, 000 m.

(d) Diameter of the Sun is 1, 400, 000, 000 m.

(e) In a galaxy there are on an average 100, 000, 000, 000 stars.

(f) The universe is estimated to be about 12, 000, 000, 000 years old.

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300, 000, 000, 000, 000, 000, 000 m.

(h) 60, 230, 000, 000, 000, 000, 000, 000 molecules are contained in a drop of water weighing 1.8 gm.

(i) The earth has 1, 353, 000, 000 cubic km of sea water.

(j) The population of India was about 1, 027, 000, 000 in March, 2001.