Bạn sai đề rồi!

75²⁰>45¹⁰.2¹⁵

Ta có: 75²⁰ = (5² . 3)²⁰ = 5⁴⁰ . 3²⁰

45¹⁰ . 25¹⁵ = (3² . 5)¹⁰ . (5²)¹⁵ = 3²⁰ . 5¹⁰ . 5³⁰ = 3²⁰ . 5⁴⁰

=> 75²⁰ = 45¹⁰ . 25¹⁵ (= 3²⁰ . 5⁴⁰)

75²⁰=45¹⁰.25¹⁵  <=> (25.3)²⁰=(5.9)¹⁰.(5²)¹⁵ <=>5⁴⁰.3²⁰=5¹⁰.3²⁰.5³⁰ <=> 5⁴⁰.3²⁰= 5⁴⁰.3²⁰

quá dễ

\(75^{20}=\left(3\cdot5^2\right)^{20}=3^{20}\cdot5^{40}\)

\(45^{10}\cdot25^{15}=\left(3^2\cdot5\right)^{10}\cdot\left(5^2\right)^{15}=3^{20}\cdot5^{40}\)

Thi trổ tài ở đâu vậy

75²⁰=75⁵x75¹⁵=5¹⁰x3⁵x3¹⁵x25¹⁵=5¹⁰x3²⁰x25¹⁵=5¹⁰x9¹⁰x25¹⁵=45¹⁰x25¹⁵

Sai đề

\(75^{20}=\left(3.5^2\right)^{20}=3^{20}.5^{40}\)

\(45^{10}.25^{15}=\left(3^2.5\right)^{10}.\left(5^2\right)^{15}=3^{20}.5^{10}.5^{30}=3^{20}.5^{40}\)

Vậy ........

co giao cho ma sao sai duoc

Ta có :

\(75^{10}.75^{10}=\left(5^{10}.3^{10}.3^{10}\right).\left(5^{10}.5^{10}.5^{10}\right)\)

\(75^{10}.75^{10}=\left(5^{10}.5^{10}.3^{10}\right).\left(5^{10}.5^{10}.3^{10}\right)\)

\(75^{10}.75^{10}=75^{10}.75^{10}\)

Vì vậy : \(75^{20}=45^{10}.5^{30}\)

\(75^{20}=3^{20}.5^{40}\)

\(45^{10}.5^{30}=3^{20}.5^{40}\)

Do đó:\(75^{20}=45^{10}.5^{30}\)(đpcm)

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

\(\frac{45^{10}\cdot5^{20}}{75^{15}}=\frac{9^{10}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot25^{15}}=\frac{3^{20}\cdot5^{30}}{3^{15}\cdot5^{30}}=3^5\)