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