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50+51+...+100 shortcut method

$1.\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x},{3}^{3}\times {3}^{5}={\left({3}^{3}\right)}^{\mathrm{x}}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}2.\mathrm{Ex}[\mathrm{ress}0.\overline{588}\mathrm{in}\mathrm{the}\mathrm{form}\mathrm{of}\frac{\mathrm{p}}{\mathrm{q}}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}3.\mathrm{Find}\mathrm{five}\mathrm{rational}\mathrm{numbers}\mathrm{between}\frac{3}{5}\mathrm{and}\frac{4}{5}$