[tex] \\ \boxed{\:a^b\cdot \:a^c=a^{b+c}}\\\\ a) \:\ 3^9\cdot \:3^6=\:3^{9+6}=\:3^{15}\\\\ b) \:\ 7^{12}\cdot \:7^3=\:7^{3+12}=\:7^{15}\\\\ c) \:\ 5^{19}\cdot \:5=\:5^{19+1}=\:5^{20}\\\\ d) \:\ 3^{23\:}:\:3^{13} => \frac{3^{23}}{3^{13}}=3^{23-13}=3^{10}\\\\ e) \:\ 7^{20}:\:7^{13} => \frac{7^{20}}{7^{13}}=7^{20-13}=7^7\\\\ f) \:\ 5^{19}:\:5 => \frac{5^{19}}{5}=5^{18}\\\\ g) \:\ \left(3^2\right)^4 = 9^4\\\\ h) \:\ (2^3)^4 = 8^4\\\\ i) \:\ (5^6)^7 = 15625^7 [/tex]
[tex] \\\\ j) \:\ 2^9 \cdot 7^9 = 2^9 \cdot 7^9\\\\ k) \:\ 5^{12}\:\cdot 3^{12} = 5^{12}\:\cdot 3^{12}\\\\ l) \:\ \:7^{21}\:\cdot \:5^{21} = \:7^{21}\:\cdot \:5^{21} [/tex]
