[latex]c)(frac{3}{2})^-^6*(frac{3}{2})^2*frac{9^4}{8^3}=(frac{3}{2})^-^6*(frac{3}{2})^2*frac{3^8}{2^9}=frac{3^-^6^+^2^+^8}{2^-^6^+^2^+^9}=frac{3^4}{2^5}=frac{81}{16}=5frac{1}{16}[/latex] [latex]d)10^4*(frac{4}{5})^-^3*(5^5)^-^1=10^4*(frac{5}{4})^3*5^-^5=10000*frac{5^-^2}{4^3}=\ frac{10000*frac{1}{25}}{64}=frac{400}{64}=frac{50}{8}=6frac{1}{4}[/latex] [latex]e)2^-^5*(frac{1}{sqrt{2}})^-^4*sqrt{8}^6=2^-^5*(sqrt{2})^4*8^3=2^-^5*2^2*2^9=\ 2^-^5^+^2^+^9=2^6=64[/latex] [latex]f)frac{(sqrt{3})^8}{(sqrt{27})^-^2}*(3^4:3^-^2)^-^2=frac{3^4}{27^-^1}*(3^6)^-^2=frac{3^4}{3^-^3}*3^-^1^2=\ 3^7*3^-^1^2=3^-^5=(frac{1}{3})^5=frac{1}{243}[/latex]
