Ta có:
\(8^5+4^7-16^3=\left(2^3\right)^5+\left(2^2\right)^7-\left(2^4\right)^3\)
\(=2^{15}+2^{14}-2^{12}\)
\(=2^4.\left(2^{11}+2^{10}-2^8\right)=16.\left(2^{11}+2^{10}-2^8\right)\)
Vì 16 chia hết cho 16 nên \(16.\left(2^{11}+2^{10}-2^8\right)\) chia hết cho 16
Do đó \(8^5+4^7-16^3\)chia hết cho 16 (đpcm)
Chúc bạn học tốt!!!
\(8^5+4^7-16^3\\ =\left(2^3\right)^5+\left(2^2\right)^7-\left(2^4\right)^3\\ =2^{15}+2^{14}-2^{12}\\ =2^{12}\cdot\left(2^3+2^2-1\right)\\ =2^{4\cdot3}\cdot\left(8+4-1\right)\\ =\left(2^4\right)^3\cdot11\\ =16^3\cdot11⋮16\)
Vậy \(8^5+4^7-16^3⋮16\)
\(8^5+4^7-16^3\)
\(=\left(2^3\right)^5+\left(2^2\right)^7-\left(2^4\right)^3\)
\(=2^{15}+2^{14}-2^{12}\)
\(=2^{12}.2^3+2^{12}.2^2-2^{12}.1\)
\(=2^{12}\left(2^3+2^2-1\right)\)
\(=2^{12}\left(8+4-1\right)\)
\(=2^{12}.11\)
\(=\left(2^4\right)^3.11\)
\(=16^3.11⋮16\rightarrowđpcm\)