\(\dfrac{9^{85}}{\left(-3\right)^{40}}=\dfrac{9^{85}}{3^{40}}=\dfrac{3^{255}}{3^{40}}=3^{215}\)

\(\frac{9^{85}}{(-3)^{40}}= \frac{\left [ (3)^{2} \right ]^{85}}{3^{40}}= \frac{3^{170}}{3^{40}}= 3^{130}\)

= 85 x 85 - 84 x 84 = 85 x 84 + 85 - 84 x 84 = 84 x 84 + 84 + 85 - 84 x 84 = (84 x 84 - 84 x 84) + 85 + 84 = 169 = 13^2

= 13^2 nhaaaaaaa

85^2 - 84^2 = (85-84).(85+84)=169=13^2

B = 2 3 . 4 2 + 3 2 . 3 2 - 40 =   169   =   13 3

C = 11 . 2 4 + 6 2 . 19 + 40 = 900 = 30 2

2 ^ 10 . 15 + 2 ^ 10 . 85

= 2 ^ 10 . ( 15 + 55 )

= 2 ^ 10 . 100

= 1024 . 100

= 102400

= 320 ^ 2

Lời giải:

\(2^{20}.15+2^{20}.85=2^{20}(15+85)=2^{20}.100=(2^{10})^2.10^2\)

\(=(2^{10}.10)^2=10240^2\)

\(2^{20}\cdot15+2^{20}\cdot85=2^{20}\cdot100=10240^2\)

3¹⁰: 3⁵

= 3 ⁵

9^8:3^2=(3^2)^8:3^2=3^16:3^2=3^16-2=3^14