INDICES, SURDS & LOGARITHMS

 $Simplify\ 9^{2x}\times27^{x-1}\div3^{2x}=$  

•  $3^{5x-1}$  

•  $3^{5x-3}$  

•  $9^{5x-1}$  

•  $9^{5x-3}$  

 $Simplify\ \frac{36p^2q^7}{18p^{-3}q^4}\times4p^5$  

•  $8p^4q^3$  

•  $8p^{10}q^7$  

•  $8p^{10}q^3$  

•  $8p^{10}q^{11}$  

 $Find\ the\ value\ of\ \frac{2\sqrt{3}+3\sqrt{2}}{2\sqrt{3\ }-3\sqrt{2}}+\frac{\sqrt{8}}{\sqrt{2}+\sqrt{3}}$  

 $Find\ the\ value\ of\ \frac{1}{\sqrt{5}-2}\ +8-\sqrt{5}$  

Without using a calculator, find the value of  $\frac{\log_527+2\log_56\ -\log_53}{\log_520\ -\log_52-1}$  

 $Solve\ the\ equation\ 2^{\log_3\left(x+1\right)}=\frac{1}{8}$