Question

[Phan Nghĩa]

Rút gọn

\(B=\frac{25^5+25^7+25^9}{5^{11}+5^{13}+5^{15}+5^{17}+5^{19}+5^{21}}\)

Answer 1

[Kiyotaka Ayanokoji]

\(B=\frac{25^5+25^7+25^9}{5^{11}+5^{13}+5^{15}+5^{17}+5^{19}+5^{21}}\)

\(B=\frac{\left(5^2\right)^5+\left(5^2\right)^7+\left(5^2\right)^9}{5^{11}+5^{13}+5^{15}+5^{17}+5^{19}+5^{21}}\)

\(B=\frac{5^{10}+5^{14}+5^{18}}{5^{11}+5^{13}+5^{15}+5^{17}+5^{19}+5^{21}}\)

\(B=\frac{5^{10}.\left(1+5^4+5^8\right)}{5^{11}.\left(1+5^2+5^4+5^6+5^8+5^{10}\right)}\)

\(B=\frac{1+5^4+5^8}{5.\left[\left(1+5^4+5^8\right)+5^2.\left(1+5^4+5^8\right)\right]}\)

\(B=\frac{1+5^4+5^8}{5.\left[\left(1+5^4+5^8\right).\left(1+5^2\right)\right]}\)

\(B=\frac{1+5^4+5^8}{5.\left(1+5^4+5^8\right).26}\)

\(B=\frac{1}{5.26}\)

\(B=\frac{1}{130}\)

Nhớ k cho m nha