\(a,\dfrac{3^{43}+3^4}{3^{39}+1}\)

\(=\dfrac{3^4\cdot\left(3^{39}+1\right)}{3^{39}+1}\)

\(=3^4\)

\(=81\)

\(b,\dfrac{3^{10}.11+3^{10}.5}{3^9.2^4}\)

\(=\dfrac{3^{10}\left(11+5\right)}{3^9.2^4}\)

\(=\dfrac{3^{10}.16}{3^9.2^4}\)

\(=\dfrac{3^{10}.2^4}{3^9.2^4}=3\)

a, A = 27.36+73.99+27.14 - 49.73

= 27(36+14)+73(99 - 49)

= 27.50 + 73.50 = 50(27+73) = 50.100 = 5000

b, B =  4 5 . 10 . 5 6 + 25 5 . 2 8 : 2 8 . 5 4 + 5 7 . 2 5

Ta có: 4 5 = 2 2 5 = 2 2 . 5 = 2 10 ; 25 5 = 5 2 5 = 5 2 . 5 = 5 10

=>  4 5 . 10 . 5 6 + 25 5 . 2 8 = 2 10 . 2 . 5 . 5 6 + 5 10 . 2 8 =  2 11 . 5 7 + 5 10 . 2 8 =  2 8 . 2 3 . 5 7 + 5 7 . 5 3 . 2 8 =  2 8 . 5 7 . 2 3 + 5 3

Ta lại có:  2 8 . 5 4 + 5 7 . 2 5 = 2 5 . 2 3 . 5 4 + 5 4 . 5 3 . 2 5 =  2 5 . 5 4 . 2 3 + 5 3

Suy ra B =  2 8 . 5 7 . 2 3 + 5 3 :[ 2 5 . 5 4 . 2 3 + 5 3 ] =  2 8 . 5 7 : 2 5 . 5 4

=  2 8 : 2 5 . 5 7 : 5 4 =  2 3 . 5 3 = 2 . 5 3 = 10 3 = 1000

a, A = 27.36+73.99+27.14 - 49.73

= 27(36+14)+73(99 - 49)

= 27.50 + 73.50 = 50(27+73) = 50.100 = 5000

b, B =  4 5 . 10 . 5 6 + 25 5 . 2 8 : 2 8 . 5 4 + 5 7 . 2 5

Ta có: 4 5 = 2 2 5 = 2 2 . 5 = 2 10 ; 25 5 = 5 2 5 = 5 2 . 5 = 5 10

=>  4 5 . 10 . 5 6 + 25 5 . 2 8 = 2 10 . 2 . 5 . 5 6 + 5 10 . 2 8 =  2 11 . 5 7 + 5 10 . 2 8 =  2 8 . 2 3 . 5 7 + 5 7 . 5 3 . 2 8 =  2 8 . 5 7 . 2 3 + 5 3

Ta lại có:  2 8 . 5 4 + 5 7 . 2 5 = 2 5 . 2 3 . 5 4 + 5 4 . 5 3 . 2 5 =  2 5 . 5 4 . 2 3 + 5 3

Suy ra B =  2 8 . 5 7 . 2 3 + 5 3 :[ 2 5 . 5 4 . 2 3 + 5 3 ] =  2 8 . 5 7 : 2 5 . 5 4

=  2 8 : 2 5 . 5 7 : 5 4 =  2 3 . 5 3 = 2 . 5 3 = 10 3 = 1000

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

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

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

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

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

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

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

`@` `\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: \(68^2+64\cdot68+32^2\)

\(=\left(68+32\right)^2\)

=10000

b: \(51\cdot49=50^2-1=2499\)

can you tách ra đc hum

\(a,=72\cdot\left(-200\right)=-14400\\ b,=\left(125\cdot8\right)\left[\left(-5\right)\left(-20\right)\right]=1000\cdot100=1000000\)

= -14400

= 1000000

\(a,=\left(123-123\right)+\left(54+46\right)=100\\ b,=\left(-64+64\right)+\left(71-111\right)=-40\)

a: =54+46=100

`a)=(6xx8xx5xx3)/(5xx5xx6xx3xx8)=(1)/5`

`b)=5/8xx(9/7+5/7)`

`=5/8xx2=10/8=5/4`

A,\(\dfrac{6x8x15}{25x6x24}=\dfrac{6x8x5x3}{5x5x6x3x8}=\dfrac{1}{5}\)