Question

Please help, no links

Answer 1

Explanation:

`\text{Use:}\\\\a^n\cdot a^m=a^(n+m)\\\\(a^n)/(a^m)=a^(n-m)\\\\(a^n)^m=a^(nm)\\\\a^(-n)=\left((1)/(a)\right)^n\\\\=============================`

`A.\ (5^3)/(5^6)=5^(3-6)=5^(-3)=\left((1)/(5)\right)^3\\\\B.\ (14^3)^6=14^(3\cdot6)=14^(18)\\\\C.\ 8^3\cdot8^6=8^(3+6)=8^9\\\\D.\ (16^6)/(16^3)=16^(6-3)=16^3\\\\E.\ (21^3)^(-6)=21^(3\cdot(-6))=21^(-18)=\left((1)/(21)\right)^(18)\\\\F.\ 100^0=1\\\\G.\ (\left((2)/(5)\right)^8)/(\left((2)/(5)\right)^6)=\left((2)/(5)\right)^(8-6)=\left((2)/(5)\right)^2\\\\H.\ (0.15)^(-2)\cdot(0.15)^4=(0.15)^(-2+4)=(0.15)^2\\\\I.\ 7^(-5)=\left((1)/(7)\right)^5`

`J.\ 4\cdot4^3=4^(1+3)=4^4`