1, 3^4

2, 5^405

3, -20/3

4, 4

                                                                             KHÔNG BÍT ĐÚNG HAY KO =>HIHIHIHI

1.

a/ 125³ : 9³ = \(\left(\frac{125}{9}\right)^3\) = \(\frac{1953125}{729}\)

b/ 32⁴. 4³ = \(\left(2^5\right)^4.\left(2^2\right)^3\) = \(2^{20}.2^6\) = \(2^{26}\) =67108864

2. \(\left(x+\frac{1}{2}\right)^2=\frac{4}{25}\)

=> \(\left(x+\frac{1}{2}\right)^{ }=\frac{2^2}{5^2}\)

=>\(\left(x+\frac{1}{2}\right)^2=\left(\frac{2}{5}\right)^2\)

=> \(x+\frac{1}{2}=\frac{2}{5}\)

=> \(x=\frac{2}{5}-\frac{1}{2}=\frac{-1}{10}\)

Vậy \(x=\frac{-1}{10}\)

(-5).8.(-2).(-125)

=[(-5).(-2)].[8.(-125)]

=10.(-1000)

=-10000

\(a,\dfrac{5^{16}\cdot27^7}{125^5\cdot9^{11}}=\dfrac{5^{16}\cdot\left(3^3\right)^7}{\left(5^3\right)^5\cdot\left(3^2\right)^{11}}\)

\(=\dfrac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}=\dfrac{5}{3}\)

\(b,\left(-0,2\right)^2\cdot5-\dfrac{2^{13}\cdot27^3}{4^6\cdot9^5}\)

\(=0,04\cdot5-\dfrac{2^{13}\cdot\left(3^3\right)^3}{\left(2^2\right)^6\cdot\left(3^2\right)^5}\)

\(=0,2-\dfrac{2^{13}\cdot3^9}{2^{12}\cdot3^{10}}\)

\(=0,2-\dfrac{2}{3}\)

\(=-\dfrac{7}{15}\)

\(c,\dfrac{5^6+2^2\cdot25^3+2^3\cdot125^2}{26\cdot5^6}\)

\(=\dfrac{5^6+2^2\cdot\left(5^2\right)^3+2^3\cdot\left(5^3\right)^2}{5^6\cdot26}\)

\(=\dfrac{5^6+4\cdot5^6+8\cdot5^6}{5^6\cdot26}\)

\(=\dfrac{5^6\left(1+4+8\right)}{5^6\cdot26}\)

\(=\dfrac{13}{26}\)

\(=\dfrac{1}{2}\)

#\(Toru\)

\(a,\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{\left(5^2\right)^8.9^7.3^7}{25^5.5^5.9^{11}}\\ =\dfrac{25^8.9^7.\left(3^2\right)^3.3}{25^5.\left(5^2\right)^2.5.9^{11}}=\dfrac{25^8.9^7.9^3.3}{25^5.25^2.5.9^{11}}\\ =\dfrac{25^8.9^{10}.3}{25^7.5.9^{11}}=\dfrac{25^7.9^{10}.25.3}{25^7.9^{10}.5.9}\\ =\dfrac{25.3}{5.9}=\dfrac{5.5.3}{5.3.3}=\dfrac{5}{3}\)

\(\dfrac{8^2.125.9^2-32.5^3.81}{20^3.3^4-6^8.5^4}\)

\(=\dfrac{2^6.5^3.3^4-2^5.5^3.3^4}{4^3.5^3.3^4-2^8.3^8.5^4}\)

\(=\dfrac{2^6.5^3.3^4-2^5.5^3.3^4}{2^6.5^3.3^4-2^8.3^8.5^4}\)

\(=\dfrac{2^5.5^3.3^4\left(2-1\right)}{2^6.5^3.3^4\left(1-2^2.3^4.5\right)}\)

\(=\dfrac{2^5.5^3.3^4.1}{2^6.5^3.3^4\left(1-810\right)}\)

\(=\dfrac{1}{2.\left(-809\right)}\)

\(=-\dfrac{1}{1618}\)

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