\(\dfrac{45^{10}\cdot5^{20}}{75^{15}}=\dfrac{\left(3^2\cdot5\right)^{10}\cdot5^{20}}{\left(3\cdot5^2\right)^{15}}=\dfrac{3^{20}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot5^{30}}=3^5=243\\ \dfrac{6^6+6^3+3^3+3^6}{-73}=\dfrac{46656+216+27+729}{-73}=-\dfrac{47628}{73}\\ \dfrac{27^7+3^{15}}{9^9-27}=\dfrac{\left(3^3\right)^7+3^{15}}{\left(3^2\right)^9-3^3}=\dfrac{3^{21}+3^{15}}{3^{18}-3^3}=\dfrac{3^{15}\left(3^6+1\right)}{3^3\left(3^{15}-1\right)}=\dfrac{3^5\cdot730}{3^{15}-1}\\ \dfrac{8^{20}+4^{20}}{4^{25}+64^5}=\dfrac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\dfrac{2^{60}+2^{40}}{2^{50}+2^{30}}=\dfrac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=2^{10}=1024\)

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

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

T khó quá!

mọi người giúp mình luôn đi ạ

C=\(\frac{6^6+6^3\cdot3^3+3^6}{-73}\)

^{C=\(\frac{53217}{-73}\)}

^{C= -729}

ta co\(\frac{6^6+6^3.3^3+3^6}{-73}\)=\(\frac{2^6.3^6+2^3.3^3.3^3+3^6}{-73}\)=\(\frac{3^6.\left(2^6+2^3+1\right)}{-73}\)=\(\frac{3^6.73}{-73}\)= \(-\left(3^6\right)\)

A=6^6+6^3+3^3+3^6/-73=2^6.3^6+2^3.3^3.3^3+3^6/-73=2^6.3^6+2^3.3^6+3^6/-73=(2^6+2^3+1).3^6/-73=73.3^6/-73=-(3^6)=...

B và C tương tự

c.\(=3\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+..+\frac{2}{99.101}\right)\)

\(=3\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=3\left(1-\frac{1}{101}\right)\)

\(=\frac{300}{101}\)

a.\(=4\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)

\(=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=4\left(1-\frac{1}{100}\right)\)

\(=\frac{99}{25}\)

cái đầu tiên 10000