Question

Simplify the expression. Help asap

Answer 1

Answer:

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

» 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:

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

Answer 2

$\large \mathfrak{ \frac{(r ^{3} )^{4} }{(r ^{3})^{8} } }$

Simplify the expression by multiplying exponents

$\large \mathfrak{ \frac{r^{12} }{r ^{24} } }$

Simplify the expression by cancelling the terms

$\large \mathfrak{ \frac{1}{r ^{12} } }$