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 \(B=\frac{5^{20}}{3^3}\)

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

Ta có: 45¹⁰.5²⁰=(3².5)¹⁰.(5²)¹⁰

                      =3²⁰.(5²)⁵.25¹⁰

                     =3¹⁵.3⁵.25⁵.25¹⁰

                     =3⁵(3¹⁵.25¹⁵)

                     =3⁵.75¹⁵

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

Ta có : \(\frac{45^{10}.5^{20}}{75^{15}}=\frac{9^{10}.5^{10}.5^{20}}{3^{15}.25^{15}}=\frac{\left(3^2\right)^{10}.5^{30}}{3^{15}.\left(5^2\right)^{15}}=\frac{3^{20}.5^{30}}{3^{15}.5^{30}}=3^5\)

\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{45^{10}.25^{10}}{75^{10}.75^5}=\frac{1125^{10}}{75^{10}.75^5}=\frac{15^{10}}{75^5}=243\)

\(M=\frac{8^{20}+4^{20}}{4^{25}+64^5}=\frac{1^{20}+1^{20}}{1^{25}+8^5}=\frac{1}{32769}\)

\(N=\frac{6^6+6^3\cdot3^3+3^6}{73}=\frac{53217}{73}=729\)

T khó quá!

a)\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(3.5^2\right)^{15}}=\frac{\left(3^2\right)^{10}.5^{10}.5^{20}}{3^{15}.\left(5^2\right)^{15}}=\frac{3^{20}.5^{30}}{3^{15}.5^{30}}=3^5=243\)

b)\(\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(3.2\right)^6.\left(2^3\right)^3}=\frac{2^{15}.3^8}{3^6.2^6.2^9}=\frac{2^{15}.3^8}{3^6.2^{15}}=3^2=9\)

tính \(\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)

bạn ơi ! đề bài

\(\frac{45^{10}20^{10}}{75^{15}}\)=\(\frac{1125^{10}}{75^5.75^{10}}\)=\(\frac{1125^{10}}{75}\)=\(\frac{1}{75^5}\)=\(\frac{15^{10}}{75^5}\)=\(\frac{15^5.15^5}{75^5}\)=\(\frac{15^5}{75}\).\(15^5\)=\(\frac{1^5}{3}\).\(15^5\)=\(\frac{1}{3}.15^5\)=\(^{5^5}\)=3125

\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(3.5^2\right)^{15}}=\frac{\left(3^2\right)^{10}.5^{10}.5^{20}}{3^{15}.\left(5^2\right)^{15}}=\frac{3^{20}.5^{30}}{3^{15}.5^{30}}=3^5=243\)