## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.2

**NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Exercise 13.2**

Ex 13.2 Class 7 Maths Question 1.

Using laws of e×ponents, simplify and write the answer in e×ponential form:

(i) 32 × 34 × 38

(ii) 615 ÷ 610

(iii) a3 × a2

(iv) 7x × 72

(v) (52)3 ÷ 53

(vi) 25 × 55

(vii) a4 × b4

(viii) (34)3

(ix) (220 ÷ 215) × 23

(x) 8t ÷ 82

Solution:

(i) 32 × 34 × 38 = 32+4+8 = 314 [am ÷ an = am+n]

(ii) 615 ÷ 610 = 615-10 = 65 [am ÷ an = am-n]

(iii) a3 × a2 = a3+2 = a5 [am × an = am+n]

(iv) 7x × 72 = 7x+2 [am × an = am+n]

(v) (52)3 ÷ 53 = 52×3 ÷ 53 = 56 ÷ 53 = 56-3 = 53 [(a3)n = amn, am ÷ an = am-n]

(vi) 25 × 55 = (2 × 5)5 = 105 [am × bm = (ab)m]

(vii) a4 × b4 = (ab)4 [am × bm = (ab)4]

(ix) (220 ÷ 215) × 23 = 220-15 × 23

=25 × 23 = 25+3 = 28

(x) 8t ÷ 82 = 8t-2 [am ÷ an = am-n]

Ex 13.2 Class 7 Maths Question 2.

Simplify and express each of the following in exponential form:

Solution:

Ex 13.2 Class 7 Maths Question 3.

Say true or false and justify your answer:

(i) 10 × 1011 = 10011

(ii) 23 > 52

(iii) 23 × 32 = 65

(iv) 320 = (1000)0

Solution:

(i) 10 × 1011 = 101+11 = 1012

RHS = 10011 = (102)11 = 1022

1012 ≠ 1022

∴ Statement is false.

(ii) 23 > 52

LHS = 23 = 8

RHS = 522 = 25

8 < 25

∴ 23 < 52

Thus, the statement is false.

(iii) 23 × 32 = 65

LHS = 233 × 32 = 8 × 9 = 72

RHS = 65 = 6 × 6 × 6 × 6 × 6 = 7776

∴ 72 ≠ 7776

∴ The statement is false.

(iv) 30 = (1000)0

⇒ 1 = 1 True [∵ a0 = 1]

Ex 13.2 Class 7 Maths Question 4.

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

(i) 108 × 192

(ii) 270

(iii) 729 × 64

(iv) 768

Solution:

(i) 108 × 192 = 2 × 2 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

=28 × 34

(iii) 729 × 64 = 3 × 3 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2

=36 × 26

Ex 13.2 Class 7 Maths Question 5.

Simplify:

Solution:

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