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.

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.

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.

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.

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.