Simplify and express each of the following in exponential form: (23 × 2)2 (23 × 2)2 Solution = (23 + 1)2 [∵am × an = am + n] = (24)2 (24)2 can be written as = (2)4 × 2... View Article
Simplify and express each of the following in exponential form: (45 × a8b3)/ (45 × a5b2) (45 × a8b3)/ (45 × a5b2) Solution = 45 – 5 × (a8 – 5 × b3 – 2) …... View Article
Simplify and express each of the following in exponential form: (a5/a3) × a8 (a5/a3) × a8 Solution = (a5 – 3) × a8 … [∵am ÷ an = am – n] = a2 × a8 =... View Article
Simplify and express each of the following in exponential form: (28 × a5)/ (43 × a3) (28 × a5)/ (43 × a3) Solution (4)3 can be expressed as = (2 × 2)3 = (22)3 (52)4 can be written as... View Article
Simplify and express each of the following in exponential form: (30 + 20) × 50 (30 + 20) × 50 Solution = (1 + 1) × 1 = (2) × 1 = 2 Answer (30 + 20) × 50 = 2... View Article
Simplify and express each of the following in exponential form: 20 + 30 + 40 20 + 30 + 40 Solution = 1 + 1 + 1 = 3 Answer 20 + 30 + 40= 3... View Article
Simplify and express each of the following in exponential form: 37/ (34 × 33) 37/ (34 × 33) Solution = 37/ (34+3) … [∵am × an = am + n] = 37/ 37 = 37 – 7 …... View Article
Simplify and express each of the following in exponential form: (3 × 72× 112)/ (21 × 112) (3 × 72 × 118)/ (21 × 113) Solution Factors of 21 = 7 × 3 The given expression can be written as = (3 ×... View Article
Simplify and express each of the following in exponential form: 254 ÷ 53 254 ÷ 53 Solution (25)4 can be expressed as = (5 × 5)4 = (52)4 (52)4 can be written as = (5)2 ×... View Article
Simplify and express each of the following in exponential form: ((52)3 × 54) ÷ 57 ((52)3 × 54) ÷ 57 Solution (52)3 can be expressed as = (5)2 × 3 [∵(am)n = amn] = 56 Then, =... View Article
Simplify and express each of the following in exponential form: (23 × 34 × 4)/ (3 × 32) (23 × 34 × 4)/ (3 × 32) Answer Factorisation of 32 = 2 × 2 × 2 × 2 × 2 = 25... View Article
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)2 (ix) (220 ÷ 215) × 23 (x) 8t ÷ 82 (i) 32 × 34 × 38 Answer We know that by the rule of multiplying the powers with the same base = am × an =... View Article
Compare the following numbers: (i) 2.7 × 1012 ; 1.5 × 108 (ii) 4 × 1014 ; 3 × 1017 (i) 2.7 × 1012 ; 1.5 × 108 Answer On comparing the given exponents of base 10, Hence 2.7 × 1012 > 1.5... View Article
Simplify: (i) (- 4)3 (ii) (-3) × (-2)3 (iii) (-3)2 × (-5)2 (iv) (-2)3 × (-10)3 (i) (– 4)3 Answer The expansion of given expression -43 is = – 4 × – 4 × – 4 = – 64 (ii)... View Article
Simplify: (i) 2 × 102 (ii) 72 × 22 (iii) 23 × 5 (iv) 3 × 44 (v) 0 × 102 (vi) 52 × 33 (vii) 24 × 32 (viii) 32 × 104 (i) 2 × 103 Answer We can express the given question as follows, = 2 × 10 × 10 × 10 = 2 × 1000 = 2000 (ii)... View Article
Express each of the following as product of powers of their prime factors: (i) 648 (ii) 405 (iii) 540 (iv) 3,600 (i) 648 Answer The prime factorisation of 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 23 × 34 (ii) 405 Answer The prime factorisation of 405 = 3 × 3... View Article
Identify the greater number, wherever possible, in each of the following. (i) 43 or 32 (ii) 53 or 32 (iii) 28 or 82 (iv) 1002 or 2100 (v) 210 or 102 (i) 43 or 34 Answer The expansion of 43 is expressed as= 4 × 4 × 4 = 64 The expansion of 34 is expressed as = 3 × 3 × 3 × 3 = 81 So from... View Article
Express each of the following numbers using exponential notation: (i) 512 (ii) 343 (iii) 729 (iv) 3125 (i) 512 Solution:- On the prime factorisation of 512, we get 512= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2... View Article
Express the following in exponential form: (i) 6 × 6 × 6 × 6 (ii) t × t (iii) b × b × b × b (iv) 5 × 5× 7 × 7 × 7 (v) 2 × 2 × a × a (vi) a × a × a × c × c × c × c × d (i) 6 × 6 × 6 × 6 Answer The given expression can be written in the exponential form as 64. (ii) t × t Answer The given expression can be... View Article
Find the value of: (i) 26 (ii) 93 (iii) 112 (iv) 54 (i) 26 (i) 26 Answer The given value can be expressed as, = 2 × 2 × 2 × 2 × 2 × 2 = 64 (ii) 93 Answer The... View Article
