a)
(-1\frac{1}{2})^4-2^{-2}=(-\frac{3}{2})^4-(\frac{1}{2})^2=\frac{81}{16}-\frac{1}{4}=\frac{81}{16}-\frac{4}{16}=\frac{77}{16}=4\frac{13}{16}
b)
{{[(2\frac{1}{2})^{-1}-2^{-2}]^{-2}=[(\frac{5}{2})^{-1}-(\frac{1}{2})^2]^{-2}=(\frac{2}{5}-\frac{1}{4})^{-2}=(\frac{8}{20}-\frac{5}{20})^{-2}=(\frac{3}{20})^{-2}=(\frac{20}{3})^2=\frac{400}{9}=44\frac{4}{9}}}
c)
{(1+3^{-1}*2\frac{1}{3})^{-1}:2^{-3}=(1+\frac{1}{3}*\frac{7}{3})^{-1}:(\frac{1}{2})^3=(1\frac{7}{9})^{-1}:\frac{1}{8}=(\frac{16}{9})^{-1}*\frac{8}{1}=\frac{9}{\not16^2}*\not8^1=\frac{9}{2}=4\frac{1}{2}}
d)
{[3^{-1}+3^{-2}+3^{-3}]^{-1}=[\frac{1}{3}+(\frac{1}{3})^2+(\frac{1}{3})^3]^{-1}=[\frac{1}{3}+\frac{1}{9}+\frac{1}{27}]^{-1}=(\frac{9+3+1}{27})^{-1}=(\frac{13}{27})^{-1}=\frac{27}{13}=2\frac{1}{13}}
e)
(-1\frac{1}{4})^2*(2\frac{1}{2})^{-2}+10^{-2}:10^{-3}=(-\frac{5}{4})^2*(\frac{5}{2})^{-2}+10^{-2-(-3)}=
=(\frac{5}{4})^2*(\frac{2}{5})^2+10^{-2+3}=(\frac{\not5^1}{\not4^2}*\frac{\not2^1}{\not5^1})^2+10^1=(\frac{1}{2})^2+10=\frac{1}{4}+10=10\frac{1}{4}
f)
{[(3^0+3^{-1})*(\frac{1}{2})^{-2}]:(\frac{1}{3})^{-3}=[(1+\frac{1}{3})*2^2]:3^3=[(\frac{3}{3}+\frac{1}{3})*4]:27=(\frac{4}{3}*4):27=\frac{16}{3}*\frac{1}{27}=\frac{16}{81}}
g)
{[(-\frac{3}{4})^{-2}+(-\frac{3}{4})^{-3}]^{-1}=[(-\frac{4}{3})^2+(-\frac{4}{3})^3]^{-1}=[\frac{16}{9}+(-\frac{64}{27})]^{-1}=(\frac{48}{27}-\frac{64}{27})^{-1}=(-\frac{16}{27})^{-1}=-\frac{27}{16}=-1\frac{11}{16}}
h)
[3^{-1}*(3^{-1}-3^{-2})]^{-1}-[3^1*(3^{-1}-1^{-1})]^{-1}=[3^{-1}*(\frac{1}{3}-(\frac{1}{3})^2)]^{-1}-[(3*(\frac{1}{3}-1)]^{-1}=
{=[3^{-1}*(\frac{3}{9}-\frac{1}{9})]^{-1}-[\not3^1*(-\frac{2}{\not3^1})]^{-1}=(\frac{1}{3}*\frac{2}{9})^{-1}-(-2)^{-1}=(\frac{2}{27})^{-1}-(-\frac{1}{2})=\frac{27}{2}+\frac{1}{2}=\frac{28}{2}=14}