Simplify 36×2×3²×10/18×5³×7
Answers
Answer:
Step-by-step explanation:
Find the value of:
(i) 26 (ii) 93
(iii) 112 (iv)54
ANSWER:
(i) 26 = 2 × 2 × 2 × 2 × 2 × 2 = 64
(ii) 93 = 9 × 9 × 9 = 729
(iii) 112 = 11 × 11 = 121
(iv)54 = 5 × 5 × 5 × 5 = 625
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Question 2:
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
ANSWER:
(i) 6 × 6 × 6 × 6 = 64
(ii) t × t= t2
(iii) b × b × b × b = b4
(iv) 5 × 5 × 7 × 7 × 7 = 52 × 73
(v) 2 × 2 × a × a = 22 × a2
(vi) a × a × a × c × c × c × c × d = a3 c4 d
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Question 3:
Express the following numbers using exponential notation:
(i) 512 (ii) 343
(iii) 729 (iv) 3125
ANSWER:
(i) 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 29
(ii) 343 = 7 × 7 × 7 = 73
(iii) 729 = 3 × 3 × 3 × 3 × 3 × 3 = 36
(iv) 3125 = 5 × 5 × 5 × 5 × 5 = 55
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Question 4:
Identify the greater number, wherever possible, in each of the following?
(i) 43 or 34 (ii) 53 or 35
(iii) 28 or 82 (iv) 1002 or 2100
(v) 210 or 102
ANSWER:
(i) 43 = 4 × 4 × 4 = 64
34 = 3 × 3 × 3 × 3 = 81
Therefore, 34 > 43
(ii) 53 = 5 × 5 × 5 =125
35 = 3 × 3 × 3 × 3 × 3 = 243
Therefore, 35 > 53
(iii) 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
82 = 8 × 8 = 64
Therefore, 28 > 82
(iv)1002 or 2100
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
2100 = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 ×1024 × 1024
1002 = 100 × 100 = 10000
Therefore, 2100 > 1002
(v) 210 and 102
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
102 = 10 × 10 = 100
Therefore, 210 > 102
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Question 5:
Express each of the following as product of powers of their prime factors:
(i) 648 (ii) 405
(iii) 540 (iv) 3,600
ANSWER:
(i) 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 23. 34
(ii) 405 = 3 × 3 × 3 × 3 × 5 = 34 . 5
(iii) 540 = 2 × 2 × 3 × 3 × 3 × 5 = 22. 33. 5
(iv) 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 24. 32. 52
Find the value of:
(i) 26 (ii) 93
(iii) 112 (iv)54
ANSWER:
(i) 26 = 2 × 2 × 2 × 2 × 2 × 2 = 64
(ii) 93 = 9 × 9 × 9 = 729
(iii) 112 = 11 × 11 = 121
(iv)54 = 5 × 5 × 5 × 5 = 625
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Question 2:
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
ANSWER:
(i) 6 × 6 × 6 × 6 = 64
(ii) t × t= t2
(iii) b × b × b × b = b4
(iv) 5 × 5 × 7 × 7 × 7 = 52 × 73
(v) 2 × 2 × a × a = 22 × a2
(vi) a × a × a × c × c × c × c × d = a3 c4 d
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Question 3:
Express the following numbers using exponential notation:
(i) 512 (ii) 343
(iii) 729 (iv) 3125
ANSWER:
(i) 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 29
(ii) 343 = 7 × 7 × 7 = 73
(iii) 729 = 3 × 3 × 3 × 3 × 3 × 3 = 36
(iv) 3125 = 5 × 5 × 5 × 5 × 5 = 55
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Question 4:
Identify the greater number, wherever possible, in each of the following?
(i) 43 or 34 (ii) 53 or 35
(iii) 28 or 82 (iv) 1002 or 2100
(v) 210 or 102
ANSWER:
(i) 43 = 4 × 4 × 4 = 64
34 = 3 × 3 × 3 × 3 = 81
Therefore, 34 > 43
(ii) 53 = 5 × 5 × 5 =125
35 = 3 × 3 × 3 × 3 × 3 = 243
Therefore, 35 > 53
(iii) 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
82 = 8 × 8 = 64
Therefore, 28 > 82
(iv)1002 or 2100
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
2100 = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 ×1024 × 1024
1002 = 100 × 100 = 10000
Therefore, 2100 > 1002
(v) 210 and 102
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
102 = 10 × 10 = 100
Therefore, 210 > 102
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Question 5:
Express each of the following as product of powers of their prime factors:
(i) 648 (ii) 405
(iii) 540 (iv) 3,600
ANSWER:
(i) 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 23. 34
(ii) 405 = 3 × 3 × 3 × 3 × 5 = 34 . 5
(iii) 540 = 2 × 2 × 3 × 3 × 3 × 5 = 22. 33. 5
(iv) 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 24. 32. 52