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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) 7^x × 7² (v) (5²)² ÷ 5³( vi) 2⁵ × 5⁵ (vii) a⁴ × b⁴ (viii) (3⁴)² (ix) (2²⁰ ÷ 2¹⁵) × 2³ (x) 8^t ÷ 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