Question

Simplify the expression. Help asap

Answer 1

`{ \tt{ \frac{ {(r}^(3) ) {}^(4) }{( {r}^(3) ) {}^(8) } }} \\`

» Let r³ be x:

`= { \tt{ \frac{ {x}^(4) }{ {x}^(8) } }} \\`

» From law of indices:

`{ \boxed{ \pmb{ \green{ \frac{ {a}^(m) }{ {a}^(n) } = {a}^((m - n)) }}}}`

» Taking a comparison from the question;

• a is x
• m is 4
• n is 8

`{ \tt{ \frac{ {x}^(4) }{ {x}^(8) } = {x}^((4 - 8)) }} \\ \\ { \underline{ \tt{ \: = {x}^( - 4) \: }}}`

» Substitute for x as r³:

`{ \tt{ = ( {r}^(3)) {}^( - 4) }} \\ = { \tt{( {r)}^((3 * - 4)) }} \\ = { \tt{ {r}^( - 12) }} \\ \\ { \boxed{ \mathfrak{ answer : \: { \tt{ \red{ \: \frac{1}{ {r}^(12) } }}}}}}`