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\(a,\frac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}\)
\(=\frac{\left(2^4\right)^3.3^{10}+2^3.3.5.\left(2.3\right)^9}{\left(2^2\right)^6.3^{12}+\left(2.3\right)^{11}}\)
\(=\frac{2^{12}.3^{10}+2^3.3.5.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3+1\right)}\)
\(=\frac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.7}=\frac{2.6}{3.7}=\frac{4}{7}\)
\(\frac{8^{11}.3^{17}}{27^{10}.9^{15}}=\frac{8^{11}.3^{17}}{3^{30}.3^{30}}=\frac{8^{11}}{3^{13}.3^{30}}=\frac{8^{11}}{3^{43}}\)
\(\frac{\left(5^4-5^3\right)^3}{125^4}=\frac{[\left(5-1\right).5^3]^3}{5^{12}}=\frac{\left(4.5^3\right)^3}{5^{12}}=\frac{64.5^9}{5^{12}}=\frac{64}{5^3}=\left(\frac{4}{5}\right)^3\)
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{40}-2^{20}+6^{20}}{6^{20}-3^{20}+3^{40}}=\frac{2^{20}.\left(2^{20}-1+3^{30}\right)}{3^{20}.\left(2^{20}-2+3^{20}\right)}=\frac{2^{20}}{3^{20}}=\left(\frac{2}{3}\right)^{20}\)
1)
a) \(\left(-48\right)^3:16^3\)
\(=\left(-48:16\right)^3\)
\(=\left(-3\right)^3\)
\(=-27.\)
b) \(\left(\frac{9}{10}\right)^6:\left(\frac{17}{-20}\right)^6\)
\(=\left(\frac{9}{10}:\frac{17}{-20}\right)^6\)
\(=\left(-\frac{18}{17}\right)^6\)
Chúc em học tốt!
\(\frac{-13^3}{\left(2^3\right)^3}:\frac{\left(-2^5\right)^4}{13^4}\)1.
a, (-48)3:163
= \(\left(\frac{-48}{16}\right)^3\)
= (-3)3
b,\(\left(\frac{9}{10}\right)^6\):\(\left(\frac{17}{-20}\right)^6\)
= \(\left(\frac{9}{10}:\frac{17}{-20}\right)^6\)
=\(\left(\frac{-18}{17}\right)^6\)
c, \(\left(\frac{-13}{8}\right)^3:\left(\frac{-32}{13}\right)^4\)
= \(\frac{-13^3}{\left(2^3\right)^3}:\frac{\left(-2^5\right)^4}{13^4}\)
= \(\frac{-13^3}{2^9}.\frac{-13^4}{2^{20}}\)
=\(\frac{13^7}{2^{29}}\)