Question:১সরল কর : `(3^3. 3^5)/3^6` 

সমাধান : `(3^3. 3^5)/3^6` 
            
        `= 3^(3 + 5)/3^6`

        `= 3^8/3^6`

        `= 3^ (8 - 6)`

        `= 3^2`

        `= 9`  (Ans.)

Question:২সরল কর : `(5^3 . 8)/(2^4 . 125)` 

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.)

Question:৩সরল কর : `(7^3 xx 7^-3)/(3 xx 3^-4)` 

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.)

Question:৪সরল  `(root(3)(7^2) . root(3)(7))/sqrt(7)` 

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.

Question:৫সরল কর `(2^-1 + 5^-1)^-1` 

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.

Question:৬সরল কর ` (2a^-1 + 3b^-1)^-1` 

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.

Question:৭ সরল কর `((a^2 b^-1)/(a^-2 b))^2` 

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.

Question:৮ সরল কর `sqrt(x^-1)y . sqrt(y^-1)z . sqrt(z^-1)x`,   `(x > 0, y > 0,  z > 0)` 

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.

Question:৯ সরল কর `(2^(n + 4) - 4.2^(n + 1))/2^(n + 2) -: 2` 

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.

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

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.