ryleighmillerr
Answered

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Simplify the expression. Help asap

Simplify The Expression Help Asap class=

Sagot :

brainsoft

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;

  • a is x
  • m is 4
  • n is 8

[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]

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