first off, let's convert the "mixed" fractions to "improper", and take it from there. Keeping in mind that anything(except 0 itself) raised at 0, is 1. Also recall that minus times minus is plus.
[tex]\bf \stackrel{mixed}{-2\frac{3}{4}}\implies -\cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{-\cfrac{11}{4}}\\\\\\ \stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \left( -2\frac{3}{4} \right)^2-\left( 1\frac{2}{3} \right)^0\implies \left(-\cfrac{11}{4} \right)^2-\left( \cfrac{5}{3} \right)^0\implies \left(-\cfrac{11}{4} \right)\left(-\cfrac{11}{4} \right)~-~1
\\\\\\
\left(\cfrac{11}{4} \right)\left(\cfrac{11}{4} \right)-1\implies \left(\cfrac{11}{4} \right)^2-1\implies \cfrac{11^2}{4^2}-1\implies \cfrac{121}{8}-1
\\\\\\
\cfrac{121-8}{8}\implies \cfrac{113}{8}\implies 14\frac{1}{8}[/tex]
