Question

Chứng minh

B = \(8^{10}+32^7\) chia hết cho 33

Answer 1

Ta có : \(B=8^{10}+32^7=\left(2^3\right)^{10}+\left(2^5\right)^7\)

\(=2^{30}+2^{35}=2^{30}.1+2^{30}.2^5=2^{30}.\left(1+2^5\right)=2^{30}.33⋮33\)

Vậy : B chia hết cho 33

Answer 2

B = 8¹⁰ + 32⁷

= (2³)¹⁰ + (2⁵)⁷

= 2³⁰ + 2³⁵

= 2³⁰.1 + 2³⁰. 2⁵

= 2³⁰. (1 + 2⁵)

= 2³⁰ . 33

Vì 33 \(⋮\)33 => 2³⁰. 33 \(⋮\)33.

Chúc bạn học tốt!

Answer 3

\(B=8^{10}+32^7=\left(2^3\right)^{10}+\left(2^5\right)^7=2^{30}+2^{35}\)

\(=2^{30}\left(2^5+1\right)=33.2^{30}\) luôn chia hết cho 33