a)

${15}^2\cdot {\left(\frac{2}{5}\right)}^2-{\left(15:1\frac{2}{3}\right)}^2=225\cdot \frac{4}{25}-{\left(15:\frac{5}{3}\right)}^2=36-{\left({\sout{15}}^3\cdot \frac{3}{{\sout{5}}^1}\right)}^2=36-3^2=36-81=-45$