Question

Simplify (2/3)3(1/5x2/3)-3(1/5)4

Answer 1

`\hspace{34em}|\\ \stackrel{\textit{\LARGE PEMDAS}}{\left( \cfrac{2}{3} \right)3 \left( \cfrac{1}{5}* \cfrac{2}{3} \right)-3\left( \cfrac{1}{5} \right)4\implies \left( 2\cdot \cfrac{3}{3} \right) \left( \cfrac{1}{5}* \cfrac{2}{3} \right)-3\left( \cfrac{1}{5} \right)4} \\\\\\ \left( 2\cdot 1 \right) \left( \cfrac{1}{5}* \cfrac{2}{3} \right)-3\left( \cfrac{1}{5} \right)4\implies 2\left( \cfrac{1}{5}* \cfrac{2}{3} \right)-3\left( \cfrac{1}{5} \right)4`

`2\left( \cfrac{2}{15} \right)-3\left( \cfrac{1}{5} \right)4\implies \cfrac{4}{15}-3\left( \cfrac{1}{5} \right)4\implies \cfrac{4}{15}-\cfrac{3\cdot 1\cdot 4}{5}\implies \cfrac{4}{15}-\cfrac{12}{5} \\\\\\ \stackrel{\textit{using the LCD of 15}}{\cfrac{(1)4~~ - ~~(3)12}{15}}\implies \cfrac{4-36}{15}\implies \cfrac{-32}{15}\implies -2(2)/(15)`