a/
$(\frac{2}{3})^3:(\frac{8}{27})^3=(\frac{2}{3})^3:[(\frac{2}{3})^3]^3$
$=(\frac{2}{3})^3:(\frac{2}{3})^9$
$=(\frac{2}{3})^{3-9}=(\frac{2}{3})^{-6}$
b/
$(\frac{-7}{5})^5:(\frac{-14}{18})^5=(\frac{-7}{5}:\frac{-14}{18})^5=(\frac{9}{5})^5$
c/
$(\frac{-1}{7})^{2018}:(\frac{1}{7})^{2018}=(\frac{-1}{7}:\frac{1}{7})^{2018}$
$=(-1)^{2018}=1$
d/
\((\frac{-5}{4})^2:(\frac{-35}{24})^2=(\frac{-5}{4}:\frac{-35}{24})^2=(\frac{6}{7})^2\)
e/
$(\frac{-1}{2})^3.(\frac{3}{2})^3=(\frac{-1}{2}.\frac{3}{2})^3=(\frac{-3}{4})^3$
f/
\(\frac{(\frac{2}{3})^3(\frac{-3}{4})^2(-1)^5}{(\frac{2}{5})^2(\frac{-5}{12})^2}=\frac{\frac{2^3.(-3)^2}{3^3.4^2}(-1)}{(\frac{2}{5}.\frac{-5}{12})^2}\\ =\frac{-\frac{2^3.3^2}{3^3.2^4}}{(\frac{-1}{6})^2}\\ =\frac{\frac{-1}{6}}{(\frac{-1}{6})^2}=\frac{1}{\frac{-1}{6}}=-6\)
g/
\(\frac{6^6+6^3.3^3+3^6}{-73}=\frac{2^6.3^6+2^3.3^3.3^3+3^6}{-73}=\frac{2^6.3^6+2^3.3^6+3^6}{-73}\\ =\frac{3^6(2^6+2^3+1)}{-73}=\frac{3^6.73}{-73}=-3^6\)
h/
\((\frac{-20}{3})^3(\frac{-18}{5})^2=\frac{-20}{3}(\frac{-20}{3}.\frac{-18}{5})^2=\frac{-20}{3}.24^2=-3840\)
i/
$A=(3^2)^2-(-2^3)^2-(-5^2)^2$
$=3^4-(-8)^2-(-25)^2=81-64-625=-608$
j/
\(A=3^2.\frac{1}{243}.81^2.\frac{1}{3^3}\\ =3^2.\frac{1}{3^5}.(3^4)^2.\frac{1}{3^3}\\ =3^2.3^{-5}.3^8.3^{-3}=3^{2+(-5)+8+(-3)}=3^2=9\)
k/
\(B=(4.2^5):(2^3.\frac{1}{16})=(2^2.2^5):(2^3.2^{-4})\\ =2^7:2^{-1}=2^{7-(-1)}=2^8\)
