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Mkey [24]
2 years ago
14

Which is the simplified form of (9c^-9)^-3 b 1/729 c^27

Mathematics
1 answer:
rosijanka [135]2 years ago
7 0

<u>ANSWER</u>

(9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729}

<u>EXPLANATION</u>

The given expression is

(9 {c}^{ - 9} )^{ - 3}

Recall that:

({a}^{m} )^{n}  =  {a}^{mn}

We use the law of exponents to get

(9 {c}^{ - 9} )^{ - 3}  = 9^{ - 3}  {c}^{ - 9 \times  - 3}

Let us multiply in the exponents to get:

(9 {c}^{ - 9} )^{ - 3}  = 9^{ - 3}  {c}^{ 27}

Recall again that:

{a}^{ - m}  =  \frac{1}{ {a}^{m} }

This implies that:

(9 {c}^{ - 9} )^{ - 3}  =  \frac{1}{ {9}^{ 3} }  \times {c}^{ 27}

We expand the power to get:

(9 {c}^{ - 9} )^{ - 3}  =  \frac{1}{9 \times 9 \times 9} \times {c}^{ 27}

(9 {c}^{ - 9} )^{ - 3}=\frac{1}{729}  \times {c}^{ 27}

We multiply out to get:

(9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729}

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