Question:সরল কর : (i) `x^3 xx x^7` (ii) `a^3 xx a xx a^5` (iii) `x^4 xx x^2 xx x^9` (iv) `m xx m^2 xx n^3 xx m^3 xx n^7` (v) `3a xx 4b xx 2a xx 5c xx 3b` (vi) `2x^2 xx y^2 xx 2z^2 xx 3y^2 xx 4x^2`
Answer সমাধান : `x^3 xx x^7` `= (x xx x xx x) xx (x xx x xx x xx x xx x xx x xx x)` `= x xx x xx x xx x xx x xx x xx x xx x xx x xx x` `= x^10` বিকল্প পদ্ধতি ; `x^3 xx x^7` `= x^3+7; [:. a^m xx a^n = a^m+n]` `= x^10` (ii) সমাধান : `a^3 xx a xx a^5` `= (a xx a xx a) xx a xx (a xx a xx a xx a xx a)` `= a xx a xx a xx a xx a xx a xx a xx a` `= a^9` বিকল্প পদ্ধতি ; `a^3 xx a xx a^5` `= a^3+1 xx a^5 ;[:. a^m xx a^n = a^m+n]` `= a^4 xx a^5` `= a^4+5` `= a^9` (iii) সমাধান : `x^4 xx x^2 xx x^9` `= (x xx x xx x xx x) xx (x xx x) xx (x xx x xx x xx x xx x xx x xx x xx x xx x)` `= (x xx x xx x xx x xx x xx x xx x xx x xx x xx x xx x xx x xx x xx x xx x)` `= x^15` বিকল্প পদ্ধতি ; `x^4 xx x^2 xx x^9` `= x^4+2 xx x^9 [:. a^m xx a^n = a^m+n]` `= x^6 xx x^9` `= x^6+9` `= x^15` (iv) সমাধান : `m xx m^2 xx n^2 xx m^3 xx n^7` `= (m xx m^2 xx m^3) xx (n^3 xx n^7)` `= (m^2+1 xx m^3) xx (n^3+7); [:. a^m xx a^n = a^m+n]` `= (m^3 xx m^3) xx n^10` `= m^3+3 xx n^10; [:. a^m xx a^n = a^m+n]` `= m^6 xx n^10` `= m^6 n^10` (v) সমাধান: `3a xx 4b xx 2a xx 5c xx 3b` `= (3a xx 2a) xx (4b xx 3b) xx 5c` `= (3 xx 2 xx a xx a) xx (4 xx 3 xx b xx b) xx 5c` `= (6 xx a^1+1) xx (12 xx b^1+1) xx 5c` `= 6a^2 xx 12b^2 xx 5c` `= (6 xx 12 xx 5) a^2 b^2 c` `= 360 a^2 b^2 c` (vi) সমাধান : `2x^2 xx y^2 xx 2z^2 xx 3y^2 xx 4x^2` `= (2x^2 xx 4x^2) xx (y^2 xx 3y^2) xx 2z^2` `= (2 xx 4 xx x^2 xx x^2) xx (3 xx y^2 xx y^2) xx 2z^2` `= (2 xx 4 xx x^2+2) xx (3 xx y^2+2) xx 2z^2` `= 8x^4 xx 3y^4 xx 2z^2` `= (8 xx 3 xx 2) x^4 y^4 z^4` `= 48 x^4 y^4 z^4`
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shorol kar : (i) `x^3 xx x^7` (ii) `a^3 xx a xx a^5` (iii) `x^4 xx x^2 xx x^9` (iv) `m xx m^2 xx n^3 xx m^3 xx n^7` (v) `3a xx 4b xx 2a xx 5c xx 3b` (vi) `2x^2 xx y^2 xx 2z^2 xx 3y^2 xx 4x^2`