Step-by-step explanation:
[tex]\text{Use:}\\\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\(a^n)^m=a^{nm}\\\\a^{-n}=\left(\dfrac{1}{a}\right)^n\\\\=============================[/tex]
[tex]A.\ \dfrac{5^3}{5^6}=5^{3-6}=5^{-3}=\left(\dfrac{1}{5}\right)^3\\\\B.\ (14^3)^6=14^{3\cdot6}=14^{18}\\\\C.\ 8^3\cdot8^6=8^{3+6}=8^9\\\\D.\ \dfrac{16^6}{16^3}=16^{6-3}=16^3\\\\E.\ (21^3)^{-6}=21^{3\cdot(-6)}=21^{-18}=\left(\dfrac{1}{21}\right)^{18}\\\\F.\ 100^0=1\\\\G.\ \dfrac{\left(\frac{2}{5}\right)^8}{\left(\frac{2}{5}\right)^6}=\left(\dfrac{2}{5}\right)^{8-6}=\left(\dfrac{2}{5}\right)^2\\\\H.\ (0.15)^{-2}\cdot(0.15)^4=(0.15)^{-2+4}=(0.15)^2\\\\I.\ 7^{-5}=\left(\dfrac{1}{7}\right)^5[/tex]
[tex]J.\ 4\cdot4^3=4^{1+3}=4^4[/tex]
