Rút gọn:
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}\)
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DG
19 tháng 3 2020
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{\left(2^2\right)^{20}-2^{20}+\left(3.2\right)^{20}}{\left(3.2\right)^{20}-3^{20}+\left(3^2\right)^{20}}=\frac{2^{20}.2^{20}-2^{20}.1+3^{20}.2^{20}}{3^{20}.2^{20}-3^{20}.1+3^{20}.3^{20}}=\frac{2^{20}.\left(2^{20}-1+3^{20}\right)}{3^{20}.\left(2^{20}-1+3^{20}\right)}=\frac{2^{20}}{3^{20}}=\left(\frac{2}{3}\right)^{20}=\frac{40}{60}=\frac{2}{3}\)
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VM
18 tháng 3 2020
Tính:
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}\)
\(=\frac{\left(2.2\right)^{20}-2^{20}+\left(2.3\right)^{20}}{\left(3.2\right)^{20}-3^{20}+\left(3.3\right)^{20}}\)
\(=\frac{2^{20}.2^{20}-2^{20}+2^{20}.3^{20}}{3^{20}.2^{20}-3^{20}+3^{20}.3^{20}}\)
\(=\frac{2^{20}.2^{20}-2^{20}.1+2^{20}.3^{20}}{3^{20}.2^{20}-3^{20}.1+3^{20}.3^{20}}\)
\(=\frac{2^{20}.\left(2^{20}-1+3^{20}\right)}{3^{20}.\left(2^{20}-1+3^{20}\right)}\)
\(=\frac{2^{20}}{3^{20}}\)
\(=\left(\frac{2}{3}\right)^{20}.\)
Chúc bạn học tốt!
DT
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\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{20}\cdot2^{20}-2^{20}+2^{20}\cdot3^{20}}{2^{20}\cdot3^{20}-3^{20}+3^{20}\cdot3^{20}}=\frac{2^{20}\left[2^{20}-1+3^{20}\right]}{3^{20}\left[2^{20}-1+3^{20}\right]}=\frac{2^{20}}{3^{20}}\)