Answer:
[tex]{ \tt{ \frac{ {(r}^{3} ) {}^{4} }{( {r}^{3} ) {}^{8} } }} \\ [/tex]
» Let r³ be x:
[tex] = { \tt{ \frac{ {x}^{4} }{ {x}^{8} } }} \\ [/tex]
» From law of indices:
[tex]{ \boxed{ \pmb{ \green{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{(m - n)} }}}}[/tex]
» Taking a comparison from the question;
[tex]{ \tt{ \frac{ {x}^{4} }{ {x}^{8} } = {x}^{(4 - 8)} }} \\ \\ { \underline{ \tt{ \: = {x}^{ - 4} \: }}}[/tex]
» Substitute for x as r³:
[tex]{ \tt{ = ( {r}^{3}) {}^{ - 4} }} \\ = { \tt{( {r)}^{(3 \times - 4)} }} \\ = { \tt{ {r}^{ - 12} }} \\ \\ { \boxed{ \mathfrak{ answer : \: { \tt{ \red{ \: \frac{1}{ {r}^{12} } }}}}}}[/tex]
