Class 7, Maths, Chapter 13, Exercise 13.2 Solutions
Q.1. Using laws of exponents, simplify and write the answer in exponential form:
(i) 32 × 34 × 38
(ii) 615 ÷ 610
(iii) a3 × a2
(iv) 7x ×72
(v) (52)2 ÷ 53
(vi) 25 × 55
(vii) a4 × b4
(viii) (34)3
(ix) (220 ÷ 215) × 23)
(x) 8t ÷ 82
Ans:
(i) 32 × 34 × 38
= (3)2 + 4 + 8 (∵ am x an = am+n)
= 314
(ii) 615 ÷ 610
= (6)15-10 (∵ am ÷ an = am-n)
= 65
(iii) a3 × a2
= (a)3+2 (∵ am x an = am + n)
= a5
(iv) 7x ×72
= (7)x+2 (∵ am x an = am + n)
(v) (52)2 ÷ 53
= 52×3 ÷ 53 (∵ (am)n = am x n)
= 56 ÷ 53 (∵ am ÷ an = am-n)
= 56-3
= 53
(vi) 25 × 55
= 25 x 55 (∵ am x bm = (a+b)m)
= (2×5)5
=105
(vii) a4 × b4
= (a x b)4 (∵ am x bm = (a+b)m)
= ab4
(viii) (34)3
= (34)3
= (3)4×3 (∵ (am)n = am x n)
= 312
(ix) (220 ÷ 215) × 23)
= (2)20-15 x 23 (∵ am ÷ an = am-n)
= 25 x 23 (∵ am x an = am +n)
= 25+3
= 28
(x) 8t ÷ 82
= (8)t-2 (∵ am ÷ an = am-n)
Q.2. Simplify and express each of the following in exponential form:
(i) $\frac{{{2}^{3}}\times {{3}^{4}}\times 4}{3\times 32}$
(ii) $\left( {{\left( {{5}^{2}} \right)}^{3}}\times {{5}^{4}} \right)\div {{5}^{7}}$
(iii) 254 ÷ 53
(iv) $\frac{3\times {{7}^{2}}\times {{11}^{8}}}{21\times {{11}^{3}}}$
(v) $\frac{{{3}^{7}}}{{{3}^{4}}\times {{3}^{3}}}$
(vi) 20 + 30 + 40
(vii) 20 + 30 + 40
(viii) (30+20) × 50
(ix) $\frac{{{2}^{8}}\times {{a}^{5}}}{{{4}^{3}}\times {{a}^{3}}}$
(x) $\left( \frac{{{a}^{5}}}{{{a}^{3}}} \right)\times {{a}^{8}}$
(xi) $\frac{{{4}^{5}}\times {{a}^{8}}{{b}^{3}}}{{{4}^{5}}\times {{a}^{5}}{{b}^{2}}}$
(xii) (23 × 2)2
Q.3. Say true or false and justify your answer:
(i) 10 × 1011 = 10011
(ii) 23 > 52
(iii) 23 × 32 = 65
(iv) 30 = (1000)0
Q.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
Ans:
(i) 108 × 192
Factors of 108 and 192 :
108 = 2 x 2 x 3 x 3 x 3
= 22 x 33
192 = 2 x 2 x 2 x 2 x 2 x 2 x 3
= 26 x 31
∴ 108 × 192 = (22 x 33) x (26 x 31)
⟹ 108 × 192 = 22 x 33 x 26 x 31
∵ am x an = am +n
⟹ 108 × 192 = 2(2+6) x 3(3+1)
⟹ 108 × 192 = 28 x 34
(ii) 270
Factor of 270:
270 = 2 x3x3x3x5 = 2 x 33 x 5
(iii) 729 × 64
The factors of 729 and 64:
729 = 3 x 3 x 3 x 3 x 3 x 3 = 36
64 = 2 x 2 x 2 x 2 x 2 x 2 = 26
∴ 729 × 64 = 36 x 26
(iv) 768
Factor of 768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3
= 28 x 3
Q.5. Simplify:
(i) $\frac{{{\left( {{2}^{5}} \right)}^{2}}\times {{7}^{3}}}{{{8}^{3}}\times 7}$
(ii) $\frac{25\times {{5}^{2}}\times {{t}^{8}}}{{{10}^{3}}\times {{t}^{4}}}$
(iii) $\frac{{{3}^{5}}\times {{10}^{5}}\times 25}{{{5}^{7}}\times {{6}^{5}}}$
