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Select the expression that is equivalent to
(6x^5)^-3


(6)/(x^2)


(1)/(6^x)


(1)/(216x^(15))


(6)/(x^(15))

User Liggliluff
by
8.2k points

1 Answer

6 votes

({ { 6x }^( 5 )) }^( -3 )

Rule :
{ (x\cdot y) }^( a )\quad =\quad { x }^( a )\cdot { y }^( a )

So if we apply this rule to the expression :


({ { 6x }^( 5 )) }^( -3 )\quad =\quad { 6 }^( -3 )\cdot { x }^( 5\cdot -3 )\quad =\quad { 6 }^( -3 )\cdot { x }^( -15 )


\boxed { { 6 }^( -3 )\cdot { x }^( -15 ) }

Let's rewrite the expression


\frac { 1 }{ { 6 }^( 3 ) } \cdot \frac { 1 }{ { x }^( 15 ) } \quad =\quad \frac { 1 }{ { 6 }^( 3 )\cdot { x }^( 15 ) }


\frac { 1 }{ 216\cdot { x }^( 15 ) }

So the answer is :


\boxed { \frac { 1 }{ 216{ x }^( 15 ) } }

(If the works are not readable there is an attachment where you can see the works better)

Select the expression that is equivalent to (6x^5)^-3 (6)/(x^2) (1)/(6^x) (1)/(216x-example-1
User James Bennett
by
8.0k points

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