\(A=\dfrac{45^{10}.5^{10}}{75^{10}}=\dfrac{5^{10}.9^{10}.5^{10}}{25^{10}.3^{10}}=\dfrac{5^{20}.3^{20}}{3^{10}.5^{20}}=3^{10}=59049\)

45^10*5^20/75^15

=5^10*9^10*5^20/(5^2)^15

=5^10*5^20*9^10/5^30

=9^10

(0.8)^5/(0.4)^6

=(0.4)^5*2^5/(0.4)^6

=2^5/(0.4)

=32/(0.4)

=80

2^15*9^4/6^6*8^3

=2^15*(3^2)^4/2^6*3^6*(2^3)^3

=2^15*3^8/2^6*3^6*2^9

=3^2

=9

\(=\frac{45^{10}\cdot5^{15}\cdot5^5}{15^{15}\cdot5^{15}}=\frac{45^{10}\cdot5^5}{15^5}=\frac{15^{10}\cdot3^{10}\cdot5^5}{15^5}=\frac{15^5\cdot15^5\cdot3^{10}\cdot5^5}{15^5}\)\(=15^5\cdot3^{10}\cdot5^5=15^5\cdot3^5\cdot3^5\cdot5^5=\left(15\cdot3\cdot3\cdot5\right)^5=675^5\)

a) 1/2 của 60 = 30

1/3 của 60 = 20

1/5 của 60 = 12

1/6 của 60 = 10

1/10 của 60 = 6

1/12 của 60 = 5

b) 15% của 60 = 9

20% của 60 = 12

50% của 60 = 30

75% của 60 = 45

c) Số 60 chia hết = Ư(60) = {1;2;3;4;5;6;10;12;15;2030;60}

\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(5.3^2\right)^{10}.5^{20}}{\left(3.5^2\right)^{15}}=\frac{5^{10}.3^{20}.5^{20}}{3^{15}.5^{30}}=\frac{5^{30}.3^{20}}{3^{15}.5^{30}}=\frac{3^5}{1}=3^5=243\)

Ta có: 45¹⁰.5²⁰=(3².5)¹⁰.(5²)¹⁰

                      =3²⁰.(5²)⁵.25¹⁰

                     =3¹⁵.3⁵.25⁵.25¹⁰

                     =3⁵(3¹⁵.25¹⁵)

                     =3⁵.75¹⁵

Do đó:  \(\frac{45^{10}.5^{20}}{75^{15}}=\frac{3^5.75^{15}}{7^{15}}=3^5\)

\(=\dfrac{\left(3^2\cdot5\right)^{10}\cdot5^{20}}{\left(3\cdot5^2\right)^{15}}=\dfrac{3^{20}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot5^{30}}=3^5=243\)

\(45^{10}\cdot5^{20}:75^{15}=\left(5.9\right)^{10}.5^{20}:\left(3.25\right)^{15}=\frac{5^{10}.9^{10}.5^{20}}{3^{15}.25^{15}}=\frac{5^{30}.3^{2.10}}{3^{15}.5^{2.15}}=\frac{5^{30}.3^{20}}{3^{15}.5^{30}}=3^5=243\)

243       

\(\frac{45^{10}\times5^{20}}{75^{15}}=\frac{\left(3^2\times5\right)^{10}\times5^{20}}{\left(5^2\times3\right)^{15}}\)\(=\frac{3^{20}\times5^{10}\times5^{20}}{5^{30}\times3^{15}}\)\(=3^5\)= 243