Question

c/tỏ rằng : 16 mũ 8 - 8 mũ 10 + 4 mũ 14 chia hết cho 208

Answer 1

\(16^8-8^{10}+4^{14}\)

\(=2^{32}-2^{30}+2^{28}\)

\(=2^{28}\cdot\left(2^4-2^2+1\right)\)

\(=2^{24}\cdot2^4\cdot13\)

\(=2^{24}\cdot208⋮208\left(đpcm\right)\)

Answer 2

16^8-8^10+4^14

= (2^4)^8-(2^3)^10+(2^2)^14

= 2^32-2^30+2^28

= 2^28(2^4-2^2+1)= 2^18 x 13 = 2^14 x 2^4 x 13 = 2^14 x 208 chia hết cho 208

Answer 3

ta có: 16⁸ - 8¹⁰ + 4¹⁴ = (2⁴)⁸ - (2³)¹⁰ + (2²)¹⁴

                                  = 2³² - 2³⁰ + 2²⁸ 

                                 = 2²⁴.(2⁸ - 2⁶ + 2⁴)

                                = 2²⁶.208 chia hết cho 208

=> đ p c m

Answer 4

\(16^8-8^{10}+4^{14}\)

=\(4^{16}-4^{15}+4^{14}\)

=\(4^{12}\left(4^4-4^3+4^2\right)\)

=\(4^{12}.208⋮208\left(ĐPCM\right)\)

Answer 5

ĐPCM là j