Sửa đề: \(5^9\cdot49^2\)

\(=\dfrac{5^{10}\cdot7^3-5^9\cdot7^4}{5^9\cdot7^3+5^9\cdot14^3}-\dfrac{2^{12}-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}\)

\(=\dfrac{5^9\cdot7^3\left(5-7\right)}{5^9\cdot7^3\left(1+8\right)}-\dfrac{2^{12}\left(1-3^4\right)}{2^{12}\left(3^6+3^5\right)}=\dfrac{-2}{9}+\dfrac{80}{972}\)

=-34/243

Câu a:

\(\frac{2^{12}.3^5-4^6.9^2}{12^6+8^4.3^5}\)

= \(\frac{2^{12}.3^5-2^{12.3^6}}{2^{12}.3^6+2^{12}.3^5}\)

= \(\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}\)

= \(\frac{2}{3.4}\)

= \(\frac16\)

Câu b:

\(\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

= \(\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)

= \(\frac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+8\right)}\)

= \(\frac{5.\left(-6\right)}{9}\)

=- 10/3

1) \(125^5:25^7\)

\(=\left(5^3\right)^5:\left(5^2\right)^7\)

\(=5^{15}:5^{14}\)

= 5

2) \(27^8:9^9\)

\(=\left(3^3\right)^8:\left(3^2\right)^9\)

\(=3^{24}:3^{18}\)

\(=3^6\)

3) \(36^5:6^8\)

\(=\left(6^2\right)^5:6^8\)

\(=6^{10}:6^8\)

\(=6^2\)

4) \(49^6:7^{10}\)

\(=\left(7^2\right)^6:7^{10}\)

\(=7^{12}:7^{10}=7^2\)

5) \(7^{20}:49^9\)

\(=7^{20}:\left(7^2\right)^9\)

\(=7^{20}:7^{18}=7^2\)

6) \(\frac{1}{2^{10}}:\frac{1}{8^3}\)

\(=\frac{1}{2^{10}}:\frac{1}{\left(2^3\right)^3}\)

\(=\frac{1}{2^{10}}:\frac{1}{2^9}=\frac{1}{2^{10}}.\frac{2^9}{1}=\frac{1}{2}\)

7) \(\left(-\frac{1}{2}\right)^{21}:\frac{1}{4^{10}}\)

\(=\frac{\left(-1\right)^{21}}{2^{21}}:\frac{1}{\left(2^2\right)^{10}}\)

\(=-\frac{1}{2^{21}}:\frac{1}{2^{20}}=-\frac{1}{2^{21}}.\frac{2^{20}}{1}\)

\(=-\frac{1}{2}\)

8) \(\frac{1}{16^5}:\left(-\frac{1}{2}\right)^{18}\)

\(=\frac{1}{\left(2^4\right)^5}:\frac{\left(-1\right)^{18}}{2^{18}}\)

\(=\frac{1}{2^{20}}:\frac{1}{2^{18}}\)

\(=\frac{1}{2^{20}}.\frac{2^{18}}{1}=\frac{1}{4}\)

9) \(\frac{1}{5^{30}}:\frac{1}{25^{14}}\)

\(=\frac{1}{5^{30}}:\frac{1}{\left(5^2\right)^{14}}\)

\(=\frac{1}{5^{30}}:\frac{1}{5^{28}}=\frac{1}{25}\)