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Chapter 13 Exponents and Powers Ex 13.2 Solutions

Question - 1 : - Using laws of e×ponents, simplify and write the answerin 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

Answer - 1 : -

(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]

Question - 2 : - Simplify and express each of the following inexponential form:

Answer - 2 : -

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

Answer - 3 : -

(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
∴ Thestatement is false.

(iv) 30 = (1000)0
⇒ 1 = 1True [∵ a0 = 1]

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

Answer - 4 : - (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

Question - 5 : - Simplify:

Answer - 5 : -


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