a) 10⁶ - 5⁷

= 2⁶ . 5⁶ - 5⁷

= 5⁶ . (2⁶ - 5)

= 5⁶ . (64 - 5)

= 5⁶ . 59 chia hết cho 59

=> đpcm

b) 81⁷ - 27⁹ - 9¹³

= (3⁴)⁷ - (3³)⁹ - (3²)¹³

= 3²⁸ - 3²⁷ - 3²⁶

= 3²⁶ .(3² - 3 - 1)

= 3²⁶ . (9 - 3 - 1)

= 3²⁴ . 3² . 5

= 3²⁴ . 9 . 5

= 3²⁴ . 45 chia hết cho 45

=> đpcm

c) 8⁷ - 2¹⁸

= (2³)⁷ - 2¹⁸

= 2²¹ - 2¹⁸

= 2¹⁸ . (2³ - 1)

= 2¹⁸ (8 - 1)

= 2¹⁷ . 2 . 7

= 2¹⁷ . 14 chia hết cho 14

=> đpcm

d) 10⁹ + 10⁸ + 10⁷

= 10⁷ . (10² + 10 + 1)

= 5⁷ . 2⁷ . (100 + 10 + 1)

= 5⁷ . 2⁶ . 2 . 111

= 5⁷ . 2⁶ . 222 chia hết cho 222

=> đpcm

A/5+10+15+...+1500

=5+10+15+...+1500 ta có:1500-5:5+1=300(số hạng)

=(5+1500)x300:2=225750

\(\left(1-\frac{1}{21}\right).\left(1-\frac{1}{28}\right).\left(1-\frac{1}{36}\right)...\left(1-\frac{1}{1326}\right)\)

\(=\frac{20}{21}.\frac{27}{28}.\frac{35}{36}...\frac{1325}{1326}\)

\(=\frac{40}{42}.\frac{54}{56}.\frac{70}{72}...\frac{2650}{2652}\)

\(=\frac{5.8}{6.7}.\frac{6.9}{7.8}.\frac{7.10}{8.9}...\frac{50.53}{51.52}\)

\(=\frac{5.6.7...50}{7.8.9...52}.\frac{8.9.10...53}{6.7.8...51}\)

\(=\frac{5.6}{51.52}.\frac{52.53}{6.7}\)

\(=\frac{5.52}{51.7}=\frac{260}{357}\)

Ủng hộ mk nha ^_-

\(a,\left[\left(0,5\right)^3\right]^n=\frac{1}{64}\Rightarrow\left(0,125\right)^n=0,125^2\Rightarrow n=2\)

\(b,\frac{64}{\left(-2\right)^{n+1}}=4\Rightarrow\left(-2\right)^{n+1}=\frac{64}{4}\Rightarrow\left(-2\right)^{n+1}=16\Rightarrow\left(-2\right)^{n+1}=\left(-2\right)^4\)

\(\Rightarrow n+1=4\Rightarrow n=3\)

\(c,\left(\frac{1}{3}\right)^{n+1}=\frac{1}{81}\Rightarrow\left(\frac{1}{3}\right)^{n+1}=\left(\frac{1}{3}\right)^4\Rightarrow n+1=4\Rightarrow n=3\)

\(d,\left(\frac{3}{4}\right)^n.\frac{1}{2}=\frac{81}{512}\Rightarrow\left(\frac{3}{4}\right)^n=\frac{81}{512}:\frac{1}{2}=\frac{81}{256}\Rightarrow\left(\frac{3}{4}\right)^n=\left(\frac{3}{4}\right)^4\Rightarrow n=4\)