\(8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{17}.\left(2^4-2\right)=2^{17}.14⋮14.\)
\(10^6-5^7=\left(2.5\right)^6-5^7=2^6.5^6-5^7=5^6.\left(2^6-5\right)=5^5.59⋮59.\)
a) Ta có : \(8^7-2^{18}=\left(2^3\right)^7-2^{17+1}\)
\(\Rightarrow8^7-2^{18}=2^{3\times7}-2^{17}\times2^1\)
\(\Rightarrow8^7-2^{18}=2^{21}-2^{17}\times2\)
\(\Rightarrow8^7-2^{18}=2^{17+4}-2^{17}\times2\)
\(\Rightarrow8^7-2^{18}=2^{17}\times2^4-2^{17}\times2\)
\(\Rightarrow8^7-2^{18}=2^{17}\left(2^4-2\right)\)
\(\Rightarrow8^7-2^{18}=2^{17}\left(16-2\right)\)
\(\Rightarrow8^7-2^{18}=2^{17}\times14\)
\(\Rightarrow\left(8^7-2^{18}\right)⋮14\left(\text{vì }14⋮14\right)\)
b) Ta có : \(10^6-5^7=\left(2\times5\right)^6-5^{6+1}\)
\(\Rightarrow10^6-5^7=2^6\times5^6-5^6\times5^1\)
\(\Rightarrow10^6-5^7=5^6\left(2^6-5^1\right)\)
\(\Rightarrow10^6-5^7=5^6\left(64-5\right)\)
\(\Rightarrow10^6-5^7=5^6\times59\)
\(\Rightarrow\left(10^6-5^7\right)⋮59\left(\text{vì }59⋮59\right)\)
