\(\dfrac{45^{10}.5^{20}}{75^{15}}\)

\(=\dfrac{9^{10}.5^{10}.5^{20}}{25^{15}.3^{15}}\)

\(=\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}\)

\(=3^5=243\)

\(=\dfrac{5^{10}\cdot3^{20}\cdot5^{20}}{\left(3\cdot5^2\right)^{15}}=\dfrac{5^{30}\cdot3^{20}}{5^{30}\cdot3^{15}}=3^5=243\)

45¹⁰x5²⁰/ 75¹⁵= 243 

nha bạn 

\(\frac{45^{10}.5^{20}}{75^{15}}\)

\(=\frac{45^{10}.\left(5^2\right)^{10}}{75^{15}}=\frac{45^{10}.25^{10}}{3^{15}.25^{15}}\)

\(=\frac{3^{10}.15^{10}}{3^{15}.25^5}=\frac{3^{10}.5^{10}}{5^5.5^5}\)

\(=3^{10}=59049\)

tick đúng nha

Bạn ghi rõ ra đi, mình ko hiểu biểu thức kia là gì

xl mình giải ra rồi bạn ơi

\(75^{20}=\left(3.5^2\right)^{20}=3^{20}.5^{40}=9^{10}.5^{10}.5^{30}=\left(9.5\right)^{10}.5^{30}=45^{10}.5^{30}\)

Ta có: \(\frac{45^{10}\cdot5^{20}}{75^{15}}\)

\(=\frac{15^{10}\cdot3^{10}\cdot5^{20}}{15^{15}\cdot5^{15}}=\frac{15^{10}\cdot3^{10}}{15^{10}\cdot15^5}\cdot3125=\frac{3^{10}\cdot5^5}{3^5\cdot5^5}=\frac{3^{10}}{3^5}=243\)

a, Thiếu 1 vế

b, Xét vế trái:

75²⁰ = 25²⁰ . 3²⁰

        = 5²⁰. 5²⁰ . 3²⁰

        = 5³⁰.5¹⁰.3¹⁰.3¹⁰

        = 5³⁰.45¹⁰ = Vế phải

=> 75²⁰ = 45¹⁰.5³⁰ (Đpcm)