$a^{-7}\ast a^{10}=a^{-7+10}=a^3$

$a^{-9}\ast a^5=a^{-9+5}=a^{-4}$

$a^{17}\ast a^{-4}\ast a^{-11}=a^{17-4-11}=a^2$

$a^{-2}:a^3=a^{-2-3}=a^{-5}$

$a^{12}:a^{-4}=a^{12-(-4)}=a^{12+4}=a^{16}$

$a^{-7}:a^{-11}=a^{-7-(-11)}=a^{-7+11}=a^4$

$a^{-12}:a^{-10}\ast a^4=a^{-12-(-10)+4}=a^{-12+10+4}=a^2$

$(a^3{)}^{-5}=a^{3\ast (-5)}=a^{-15}$

$(a^{-12}{)}^{-2}=a^{-12\ast (-2)}=a^{24}$

$(a^{-3}{)}^4:(a^{-2}{)}^5:(a^{-1}{)}^{-7}=a^{-3\ast 4}:a^{-2\ast 5}:a^{-1\ast (-7)}=a^{-12}:a^{-10}:a^7=a^{-12-(-10)-7}=a^{-12+10-7}=a^{-9}$

$(m^{-3}{n}^4{p}^7{)}^{-4}=m^{-3\ast (-4)}{n}^{4\ast (-4)}{p}^{7\ast (-4)}=m^{12}{n}^{-16}{p}^{-28}$

$(a^{-1}{b}^{-2}{)}^{-3}=a^{-1\ast (-3)}{b}^{-2\ast (-3)}=a^3{b}^6$

$(x^3{y}^{-4}{)}^5\ast (x^{-2}{y}^{-3}{)}^3=x^{3\ast 5}{y}^{-4\ast 5}\ast x^{-2\ast 3}{y}^{-3\ast 3}=x^{15}{y}^{-20}\ast x^{-6}{y}^{-9}=x^{15-6}{y}^{-20-9}=x^9{y}^{-29}$

$(\frac{a^{11}{b}^{-7}}{c^{-3}{d}^4}{)}^{-3}=\frac{a^{11\ast (-3)}{b}^{-7\ast (-3)}}{c^{-3\ast (-3)}{d}^{4\ast (-3)}}=\frac{a^{-33}{b}^{21}}{c^9{d}^{-12}}=a^{-33}{b}^{21}{c}^{-9}{d}^{12}$

$(\frac{a^{-7}}{b^5}{)}^{-3}\ast (\frac{a^4}{b^{-7}}{)}^{-5}=\frac{a^{-7\ast (-3)}}{b^{5\ast (-3)}}\ast \frac{a^{4\ast (-5)}}{b^{-7\ast (-5)}}=\frac{a^{21}}{b^{-15}}\ast \frac{a^{-20}}{b^{35}}=\frac{a^{21-20}}{b^{-15+35}}=\frac{a}{b^{20}}=a{b}^{-20}$