Question

Tính giá trị biểu thức sau:

\(\frac{2^{20}.27^3+30.4^9.9^4}{6^9.4^5+12^{10}}\)

Học thầy không tày học bạn!

Answer 1

Ta có:

\(\frac{2^{20}\cdot27^3+30\cdot4^9\cdot9^4}{6^9\cdot4^5+12^{10}}=\frac{2^{20}\cdot\left[3^3\right]^3+2\cdot3\cdot5\cdot\left[2^2\right]^9\cdot\left[3^2\right]^4}{2^9\cdot3^9\cdot\left[2^2\right]^5+3^{10}\cdot\left[2^2\right]^{10}}=\frac{2^{20}\cdot3^{3\cdot3}+2\cdot3\cdot5\cdot2^{2\cdot9}\cdot3^{2\cdot4}}{2^9\cdot3^9\cdot2^{2\cdot5}+3^{10}\cdot2^{2\cdot10}}\)

\(=\frac{2^{20}\cdot3^9+2\cdot3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+3^{10}\cdot2^{20}}=\frac{2^{20}\cdot3^9+2^{19}\cdot3^9\cdot5}{2^{19}\cdot3^9+3^{10}\cdot2^{20}}=\frac{2^{19}\cdot3^9\left[2+5\right]}{2^{19}\cdot3^9\left[1+3\cdot2\right]}=\frac{2+5}{1+6}=\frac{7}{7}=1\)