#)Giải :

c) \(\frac{45^{10}.5^{10}}{75^{10}}=\frac{\left(15.3\right)^{10}.5^{10}}{\left(15.5^{10}\right)}=\frac{15^{10}.3^{10}.5^{10}}{15^{10}.5^{10}}=3^{10}\)

\(\frac{\left(45.5\right)^{10}}{75}=\frac{225^{10}}{75}=3^{10}\)

\(C=\frac{45^{10}.5^{10}}{75}=\frac{225^{10}}{75}=\frac{225.225^9}{75}=\frac{75.3.225^9}{75}=3.225^9\)

Bài làm

\(A=\frac{45^{10}\cdot5^{20}}{75^{15}}\)

\(A=\frac{\left(3^2\right)^{10}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot\left(5^2\right)^{15}}\)

\(A=\frac{3^{20}\cdot5^{30}}{3^{15}\cdot5^{30}}\)

\(A=3^5\)

Vậy \(A=3^5\)

\(B=\frac{2^{15}\cdot5^{20}}{6^6\cdot8^3}\)

\(B=\frac{2^{15}\cdot5^{20}}{2^6\cdot3^3\cdot\left(2^3\right)^3}\)

\(B=\frac{2^{15}\cdot5^{20}}{2^{15}\cdot3^3}\)

\(B=\frac{5^{20}}{3^3}\)

Vậy \(B=\frac{5^{20}}{3^3}\)

=(45.5)^10/75^10

=(225/75)^10

=3^10

=59049

\(\frac{45^{10}\cdot5^{10}}{75^{10}}=\frac{3^{10}\cdot15^{10}\cdot5^{10}}{75^{10}}=\frac{3^{10}\cdot3^{10}\cdot5^{10}\cdot5^{10}}{3^{10}\cdot25^{10}}=\frac{3^{10}\cdot3^{10}\cdot5^{10}\cdot5^{10}}{3^{10}\cdot5^{10}\cdot5^{10}}=\frac{3^{20}\cdot5^{20}}{3^{10}\cdot5^{20}}=3^{10}\)

45^10 x 5^20 / 75^15

= ( 3^2 x 5)^10 x 5^20 / ( 3 x 5^2)^15

= 3^20 x 5^10 x 5^20 / 3^15 x 5^30

= 3^5

= 243

p/s : theo mk thì lm như vậy đó

1/3^15

a: =25(15+45*3)

=25*150

=3750

b: \(=-10\left(25+75-50\right)=-10\cdot50=-500\)

c: =>3^x-2=27

=>x-2=3

=>x=5

d: =>2x-5=-4

=>2x=1

=>x=1/2

e: =>2(x-1)^2=32

=>(x-1)^2=16

=>x-1=4 hoặc x-1=-4

=>x=-3 hoặc x=5

f:  =>25(x+3)=75

=>x+3=3

=>x=0

a) 125-(-75)+32-(48+32) = 125 + 75 + 32 - 48 - 32 = 200 - 48 = 152

b) 47.347+347.(-47) = 347.( 14 - 47 ) = 347 . 0 = 0

c) x-10=-14

x = -14 +10

x = -4

d) 15 + x = 13

x = 13 - 15

x = -2

e) 25 . x = -75

x = -75/25

x = -3

g) 5x - 16 = -46

5x = -46 + 16

5x = - 30

x = -6

i) 3x - (-11) = -4

3x + 11 = -4

3x = -4 - 11

3x = -15

x = -5

hok tốt!!

 Các cặp phân số đối nhau là:

\(\frac{{ - 5}}{6}\) và \(\frac{5}{6}\) (vì \(\frac{{ - 5}}{6}+\frac{5}{6}=0\))

\(\frac{{ - 40}}{{ - 10}}\) và \(\frac{{40}}{{ - 10}}\) (vì \(\frac{{ - 40}}{{ - 10}}+\frac{{40}}{{ - 10}}=4+(-4)=0\))

\(\frac{5}{6}\) và \(\frac{{10}}{{ - 12}}\) (vì \(\frac{5}{6} +\frac{{10}}{{ - 12}}=0\))

\(-\dfrac{5}{6};\dfrac{5}{6}\)

\(\dfrac{-40}{-10};\dfrac{40}{-10}\)

\(\dfrac{10}{-12};\dfrac{5}{6}\)