Select the expression that is equivalent to (6x^5)^-3 (6)/(x^2) (1)/(6^x) (1)/(216x^(15)) (6)/(x^(15))

Question

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


`(6)/(x^2)`


`(1)/(6^x)`


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


`(6)/(x^(15))`

Answer 1

`({ { 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)