ANSWER
[tex](9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729} [/tex]
EXPLANATION
The given expression is
[tex](9 {c}^{ - 9} )^{ - 3} [/tex]
Recall that:
[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]
We use the law of exponents to get
[tex](9 {c}^{ - 9} )^{ - 3} = 9^{ - 3} {c}^{ - 9 \times - 3} [/tex]
Let us multiply in the exponents to get:
[tex](9 {c}^{ - 9} )^{ - 3} = 9^{ - 3} {c}^{ 27} [/tex]
Recall again that:
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
This implies that:
[tex](9 {c}^{ - 9} )^{ - 3} = \frac{1}{ {9}^{ 3} } \times {c}^{ 27} [/tex]
We expand the power to get:
[tex](9 {c}^{ - 9} )^{ - 3} = \frac{1}{9 \times 9 \times 9} \times {c}^{ 27}[/tex]
[tex](9 {c}^{ - 9} )^{ - 3}=\frac{1}{729} \times {c}^{ 27} [/tex]
We multiply out to get:
[tex](9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729} [/tex]
