Question

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

Answer 1

ANSWER

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

EXPLANATION

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:

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