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Exponents and Powers
Say true or false and justify your answer:
(i) 10 × 1011 = 10011 (ii) 23 > 52
(iii) 23 × 32 = 65 (iv) 30 = (1000)0
(i) 10 × 1011 = 10011
L.H.S. = 10 × 1011 = 1011 + 1 (am × an = am+n)
= 1012
R.H.S. = 10011 = (10 ×10)11= (102)11
= 102 × 11 = 1022 (am)n = amn
As L.H.S. ≠ R.H.S.,
Therefore, the given statement is false.
(ii) 23 > 52
L.H.S. = 23 = 2 × 2 × 2 = 8
R.H.S. = 52 = 5 × 5 = 25
As 25 > 8,
Therefore, the given statement is false.
(iii) 23 × 32 = 65
L.H.S. = 23 × 32 = 2 × 2 × 2 × 3 × 3 = 72
R.H.S. = 65 = 7776
As L.H.S. ≠ R.H.S.,
Therefore, the given statement is false.
(iv) 30 = (1000)0
L.H.S. = 30 = 1
R.H.S. = (1000)0 = 1 = L.H.S.
Therefore, the given statement is true.
Sponsor Area
Simplify:
(i) 2 × 103 (ii) 72 × 22
(iii) 23 × 5 (iv) 3 × 44
(v) 0 × 102 (vi) 52 × 33
(vii) 24 × 32 (viii) 32 × 104
Simplify:
(i) (− 4)3
(ii) (− 3) × (− 2)3
(iii) (− 3)2 × (− 5)2
(iv)(− 2)3 × (−10)3
Compare the following numbers:
(i) 2.7 × 1012; 1.5 × 108
(ii) 4 × 1014; 3 × 1017
Say true or false and justify your answer:
(i) 10 × 1011 = 10011 (ii) 23 > 52
(iii) 23 × 32 = 65 (iv) 30 = (1000)0
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
Write the following numbers in the expanded forms:
279404, 3006194, 2806196, 120719, 20068
Find the number from each of the following expanded forms:
(a) 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100
(b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100
(c) 3 × 104 + 7 × 102 + 5 × 100
(d) 9 × 105 + 2 × 102 + 3 × 101
Sponsor Area
Sponsor Area