Question

Rút gọn:

A=\(\dfrac{4^{10}+8^4}{4^5+8^6}\)

B=\(\dfrac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}\)

Answer 1

\(A=\dfrac{4^{10}+8^4}{4^5+8^6}\)

\(A=\dfrac{2^{20}+2^{12}}{2^{10}+2^{18}}=\dfrac{\left(2^8+1\right).2^{12}}{\left(1+2^8\right).2^{10}}\)

\(=\dfrac{\left(256+1\right).2^2}{1+256}=\dfrac{257.2^2}{257}=2^2\)

\(B=\dfrac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}\)

\(=\dfrac{1+81+6561+3^{12}}{1+9+81+729+6561+59049+3^{12}+3^{14}}\)

\(=\dfrac{6643+3^{12}}{91+719+6561+59049+3^{12}+3^{14}}\)

\(=\dfrac{6643+3^{12}}{66430+3^{12}+3^{14}}\)

P/s : Nổi hứng lên thì lm chứ k bt đúng hay sai :V

Answer 2

4¹⁰+8⁴ _________

4⁵+8⁶

= 2²⁰+2¹²

________

2¹⁰2⁸+1

=2¹².(2⁸+1) ___________

2¹⁰.(2⁸+1)

=2¹²/2¹⁰=2²=4