\(4^{10}.8^{15}=2^{20}.2^{45}=2^{65}\)

\(4^{15}.5^{30}=2^{30}.5^{30}=10^{30}\)

\(27^{16}:9^{10}=3^{48}:3^{20}=3^{28}\)

\(72^3.54^2=2^9.3^6.2^2.3^6=2^{11}.3^{12}\)

\(108^4=2^8.3^{12}\)

\(3^{10}.11+3^{10}.5=3^{10}.\left(11+5\right)=3^{10}.16\)

\(3^9.2^4=3^9.2^4\)

`@` `\text {Ans}`

`\downarrow`

`4^10*8^15`

`= (2^2)^10 * (2^3)^15`

`= 2^20 * 2^45`

`=`\(2^{20+45}=2^{65}\)

`4^15 * 5^30`

`= (2^2)^15 * 5^30`

`= 2^30 * 5^30`

`= (2*5)^30`

`= 10^30`

`27^16 \div 9^10`

`= (3^3)^16 \div (3^2)^10`

`= 3^48 \div 3^20`

`=`\(3^{48-20}=3^{28}\)

`A = `\(72^3\cdot54^2\cdot108^4\)

`= 2^9 * 3^6 * 3^4 * 3^2 * 2^2 * 3^8 * 3^4 * 2^4 * 2^4`

`=`\(\left(2^9\cdot2^2\cdot2^4\cdot2^4\right)\cdot\left(3^6\cdot3^4\cdot3^2\cdot3^8\cdot3^4\right)\)

`= 2^19 * 3^24`

`B = 3^10 * 11 + 3^10 * 5 + 3^9 * 2^4`

`= 3^9 * (11*3 + 5*3 + 2^4)`

`= 3^9 * (33 + 15 + 16)`

`= 3^9 * 64`

`= 27^3 * 4^3`

`= (27 * 4)^3`

`= 108^3`

a)  5 69 : 5 67 - 3 40 : 3 39  = 5 2 - 3 1  = 25 – 3 = 22

a) 5 69   :   5 67   –   3 40   :   3 39   =   5 2   –   3 1  = 25 – 3 = 22

b) 155 – [ 2 . ( 30 + 5 – 26 ) . ( 24 : 3 )]

= 155 – [ 2 . 9 . 8 ] = 155 – 144 = 11

c) 37 . 143 + 37 . 57 + 1300

= (37 . 143 + 37.57) + 1300

= 37.(143+ 57) + 1300

= 37. 200 + 1300

= 7400 + 1300

8700.

a)  3 4 : 2 3 : 3 5 = 3 4 . 3 2 . 5 3 = 15 8

b)  3 4 : 2 3 : 3 5 = 3 4 : 2 3 . 5 3 = 3 4 : 10 9 = 3 4 . 9 10 = 27 40

a)  3 4 − − 1 2 = 3 4 − 1 2 = 3 4 − 2 4 = 1 4

b)  3 8 − 4 5 − − 17 40 = 15 40 − 32 40 + 17 40 = 0

a)  3 4 + 0,5 − 1 1 3 = 3 4 + 1 2 − 4 3 = 9 12 + 6 12 − 16 12 = − 1 12 .

b)  − 15 18 + 6 9 − 1 4 = − 5 6 + 2 3 − 1 4 = − 10 12 + 8 12 − 3 12 = − 5 12 .

a)  3 8 + − 5 8 − 1 8 = 3 − 5 − 1 8 = − 3 8

b)  3 4 − − 1 2 + 1 6 = 9 12 + 6 12 + 2 12 = 17 12

a)  − 7 8 + 5 − 12 + 3 4 = − 21 24 + − 10 24 + 18 24 = − 13 24

b)  21 49 + − 7 5 + 34 85 = 3 7 + − 7 5 + 2 5 = − 4 7