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m)129 X 645. Simplify:(2) ²78x725x52xtno10'xt"3 x 105 x 255x63.5 DECIMAL NUMBER SYSTEM |
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Answer» (i) ((25)2× 73)/ (83× 7) Solution:- 83can be written as = (2 × 2 × 2)3 = (23)3 We have, = ((25)2× 73)/ ((23)3× 7) = (25 × 2× 73)/ ((23 × 3× 7) … [∵(am)n= amn] = (210× 73)/ (29× 7) = (210 – 9× 73 – 1) … [∵am÷ an= am – n] = 2 × 72 = 2 × 7 × 7 = 98 (ii) (25 × 52× t8)/ (103× t4) Solution:- 25 can be written as = 5 × 5 = 52 103can be written as = 103 = (5 × 2)3 = 53× 23 We have, = (52× 52× t8)/ (53× 23× t4) = (52 + 2× t8)/ (53× 23× t4) … [∵am× an= am + n] = (54× t8)/ (53× 23× t4) = (54 – 3× t8 – 4)/ 23… [∵am÷ an= am – n] = (5 × t4)/ (2 × 2 × 2) = (5t4)/ 8 (iii) (35× 105× 25)/ (57× 65) Solution:- 105can be written as = (5 × 2)5 = 55× 25 25 can be written as = 5 × 5 = 52 65can be written as = (2 × 3)5 = 25× 35 Then we have, = (35× 55× 25× 52)/ (57× 25× 35) = (35× 55 + 2× 25)/ (57× 25× 35) … [∵am× an= am + n] = (35× 57× 25)/ (57× 25× 35) = (35 – 5× 57 – 7× 25 – 5) = (30× 50× 20) … [∵am÷ an= am – n] = 1 × 1 × 1 = 1 |
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