(Solved): some of the answers I got do not seem correct. Please check. Solve the equation 1. 162k=641 Need ...

Solve the equation 1. $16^{2k}=\frac{1}{64}$ Need to show all work! All problems 7 points each 2. $32^{2p-2}\ast 8^p={\left(\frac{1}{2}\right)}^{2p}$ 3. $4^{3k-3}\cdot 4^{2-2k}=16^{-k}$ 4. $9^{-2x}\ast {\left(\frac{1}{243}\right)}^{3x}=243^{-x}$ 5. $30-6e^{-0.1x}=20$ 6. $150=75\left(1+29e^{-0.8t}\right)$ 7. $2000e^{0.1t}=4000$ Find the $x$-int and $y$-int for the following - 8. $y={\log }_3(x+9)-5$ 9. $y={\log }_2(x+1)-3$ You remember average rate of change??? Kind of a slope thing, right? 10. Find the average rate of change for $\mathrm{f}(\mathrm{x})={\log }_2(x+1)-5$ for $0\le x\le 15$