a) 

\(4^{10}\cdot8^{15}=2^{20}\cdot2^{45}=2^{65}\)

b)

\(27^{16}\cdot9^{10}=3^{48}\cdot3^{20}=3^{68}\)

a) 4¹⁰ . 8¹⁵ = (2²)¹⁰ . (2³)¹⁵ = 2²⁰ . 2⁴⁵ = 2⁶⁵
b) 27¹⁶ . 9¹⁰ = (3³)¹⁶ .(3²)¹⁰=3⁴⁸ . 3²⁰ = 3⁶⁸
c) \(\frac{2^{10}\cdot13+2^{10}\cdot65}{28\cdot104}=\frac{2^{10}\cdot13\cdot\left(1+5\right)}{2^5\cdot7\cdot13}=\frac{2^5\cdot6}{7}=\frac{192}{7}\)

\(\frac{2^{10}.13.2^{10}.65}{2^8.104}=\frac{1024.13.1024.65}{256.104}\)

\(=\frac{1024.13.65}{256.104}=\frac{865280}{26642}\)

\(=32,5\)

\(\frac{2^{10}.13.2^{10}.65}{2^8.104}=\frac{2^{20}.13.65}{2^8.2^3.13}\)

\(=\frac{2^{20}.13.65}{2^{11}.13}\)

\(=2^9.65\)

\(=512.65\)

\(=33280\)

\(\frac{2^{10}.13.2^{10}.65}{2^8.104}=\frac{2^{20}.13^2.5}{2^{11}.13}=2^9.13.5=33280\)

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tích nha 

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ko biết nha

\(\frac{2^{10}.13.2^{10}.65}{2^8.104}\)

\(=\frac{2^{20}.13.5.13}{2^8.2^3.13}\)

\(=\frac{2^{20}.13^2.5}{2^{11}.13}\)

\(=2^9.13.5\)

\(\left(2^{10}\cdot65+13\cdot2^{10}\right):\left(2^8\cdot104\right)\)

\(=\frac{2^{10}\cdot65+13\cdot2^{10}}{2^8\cdot104}\)

\(=\frac{2^{10}\cdot\left(65+13\right)}{2^8\cdot2^3\cdot13}\)

\(=\frac{2^{10}\cdot78}{2^{11}\cdot13}\)

\(=\frac{2^{10}\cdot2\cdot3\cdot13}{2^{11}\cdot13}\)

\(=\frac{2^{11}\cdot3\cdot13}{2^{11}\cdot13}\)

\(=3\)

bài 2

\(2^x\cdot7=224\)

\(\Rightarrow2^x=224\div7\)

\(\Rightarrow2^x=32\)

\(\Rightarrow2^x=2^5\)

\(\Rightarrow x=5\)

\(\left(3^x+5\right)^2=289\)

\(\Rightarrow\left(3^x+5\right)^2=17^2\)

\(\Rightarrow3^x+5=17\)

\(\Rightarrow3^x=17-5\)

\(\Rightarrow3^x=12\)

\(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)

Xét : 210 . 13 + 210. 65 = 210 . ( 13 + 65 ) = 210 . 78 

         2⁸  . 104 = 2⁸ . ( 2² . 26 ) = 2⁸. 2². 26 = 2¹⁰.26

có : \(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)= \(\frac{2^{10}.78}{2^{10}.26}\)= \(\frac{78}{26}\)= 3

\(\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}.\left(13+65\right)}{2^8.104}=\frac{2^{10}.78}{2^8.104}\)

\(=\frac{2^2.39}{52}=\frac{2^2.39}{2^2.13}\)

\(=\frac{39}{13}\)

\(=3\)

\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)

=>\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

=>\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)

=>\(A=\frac{1}{3}-\frac{1}{21}\)

=>\(A=\frac{2}{7}\)