1. Question:সরল কর : `(3^3. 3^5)/3^6` 

    Answer
    সমাধান : `(3^3. 3^5)/3^6` 
                
            `= 3^(3 + 5)/3^6`
    
            `= 3^8/3^6`
    
            `= 3^ (8 - 6)`
    
            `= 3^2`
    
            `= 9`  (Ans.)

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  2. Question:সরল কর : `(5^3 . 8)/(2^4 . 125)` 

    Answer
    সমাধান : `(5^3 . 8)/(2^4 . 125)`
    
                  `= (5^3 . 2^3)/(2^4 . 5^3)`
    
                  `= 5^(3-3). 2^(3-4)`
    
                  `= 5^0 . 2^-1`
    
                  `= 1 . 1/2`
    
                  `= 1/2`   (Ans.)

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  3. Question:সরল কর : `(7^3 xx 7^-3)/(3 xx 3^-4)` 

    Answer
    সমাধান : `(7^3 xx 7^-3)/(3 xx 3^-4)`
    
                 `= 7^(3 - 3)/ 3^(1 - 3)`
    
                 `= 7^0/3^-3`
    
                 `= 1/3^-3`
    
                 `= 1 xx 3^3`
    
                 `= 27`  (Ans.)

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  4. Question:সরল `(root(3)(7^2) . root(3)(7))/sqrt(7)` 

    Answer
    সমাধান:  `(root(3)(7^2) . root(3)(7))/sqrt(7)`
                `= ((7^2)^(1/3) . 7^(1/3))/7^(1/2)`
    
                `= 7^(2/3 + 1/3 - 1/2)`
    
                `= 7^((4 + 2 - 3)/6)`
    
                `= 7^(3/6)`
    
                `= 7^(1/2)`
    
                `= sqrt (7)`    Ans.

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  5. Question:সরল কর `(2^-1 + 5^-1)^-1` 

    Answer
    সমাধান `(2^-1 + 5^-1)^-1`
    
             `= (1/2 + 1/5)^-1`
    
             `= ((5 + 2)/10)^-1`
    
             `= (7/10)^-1`
    
             `= 1/7`
    
             `= 1 xx 10/7`
    
             `= 10/7`  Ans.

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  6. Question:সরল কর ` (2a^-1 + 3b^-1)^-1` 

    Answer
    সমাধান ` (2a^-1 + 3b^-1)^-1`
    
             `= (2 xx 1/a + 3 xx 1/b)^-1`
    
             `= (2/a + 3/b)^-1`
    
             `= ((2b + 3a)/(ab))^-1`
    
             `= 1/((2b + 3a)/(ab))`
    
             `= 1 xx (ab)/(3a + 2b)`
    
             `= (ab)/(3a + 2b)`   Ans.

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  7. Question: সরল কর `((a^2 b^-1)/(a^-2 b))^2` 

    Answer
    সমাধান `((a^2 b^-1)/(a^-2 b))^2`
    
             `= (a^(2 + 2) b^(- 1 - 1))^2`
    
             `= (a^4 b^-2)^2`
    
             `= a^8 b^-4`
    
             `= a^8/b^4`  Ans.

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  8. Question: সরল কর `sqrt(x^-1)y . sqrt(y^-1)z . sqrt(z^-1)x`, `(x > 0, y > 0, z > 0)` 

    Answer
    সমাধান: `sqrt(x^-1)y . sqrt(y^-1)z . sqrt(z^-1)x`
    
              `= (x^-1 y)^(1/2) (y^-1 z)^(1/2) (z^-1 x)^(1/2)`
    
              `= (x^-1 y . y^-1 z . z^-1 x)^(1/2)`
    
              `= (x^(- 1 + 1) . y^(1 - 1) . z^(1 - 1))^(1/2)`
    
              `= (x^0 . y^0 . z^0)^(1/2)`
    
              `= (1 xx 1 xx 1)^(1/2)`
    
              `= 1`   Ans.বিকল্প সমাধান: `sqrt(x^-1)y . sqrt(y^-1)z . sqrt(z^-1)x`
    
              `= sqrt(1/x).y sqrt(1/y).z sqrt(1/z).x`
    
              `= sqrt(y/x) . sqrt(z/y) . sqrt(x/z)`
    
              `= sqrt(y)/sqrt(x) . sqrt(z)/sqrt(y) . sqrt(x)/sqrt(z)`
    
              `= 1` Ans.

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  9. Question: সরল কর `(2^(n + 4) - 4.2^(n + 1))/2^(n + 2) -: 2` 

    Answer
    সমাধান: `(2^(n + 4) - 4.2^(n + 1))/(2^(n + 2) -: 2)` 
    
              `= (2^n xx 2^4 - 4 xx 2^n xx 2^1)/(2^(n + 2) -: 2^1)`
    
              `= (2^n xx 16 - 8 xx 2^n)/2^(n + 2 - 1)`
    
              `= (2^n (16 - 8))/2^(n + 1)`
    
              `= (2^n xx 8)/(2^n xx 2^1)`
    
              `= 8/2`
    
              `= 4`  Ans.

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  10. Question:১০. সরল কর: `(3^(m + 1))/((3^m)^(m - 1)) -: (9^(m + 1))/((3^(m - 1))^(m + 1))` 

    Answer
    সমাধান: `(3^(m + 1))/((3^m)^(m - 1)) -: (9^(m + 1))/((3^(m - 1))^(m + 1))`
    
              `= (3^(m + 1))/(3^(m^2 - m)) -: ((3^2)^(m + 1))/(3^((m - 1)(m + 1)))`
    
              `= (3^(m + 1))/(3^(m^2 - m)) -: (3^(2m + 2))/(3^(m^2 - 1)`
    
              `= 3^(m + 1 - m^2 + m) -: 3^(2m + 2 - m^2 + 1)`
    
              `= 3^(2m - m^2 + 1) -: 3^(2m - m^2 + 3)`
    
              `= 3^((2m - m^2 + 1)-(2m - m^2 + 3))`
    
              `= 3^(2m - m^2 + 1 - 2m + m^2 - 3)`
    
              `= 3^(-2)`
    
              `= 1/3^2`
    
              `= 1/9`  Ans.

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