What is factor (-1/(3^2))^{-3} ?

The solution to factor (-1/(3^2))^{-3} is -729

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factor (-1/(3^2))^{-3}

factor

(- \frac{1}{3 ^{2}})^{- 3}

- 729

Solution steps

(- \frac{1}{3 ^{2}})^{- 3}

Apply exponent rule:

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

= \frac{1}{( - \frac{1}{3 ^{2}} ) ^{3}}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- \frac{1}{3 ^{2}})^{3} = - (\frac{1}{3 ^{2}})^{3}

= \frac{1}{- ( \frac{1}{3 ^{2}} ) ^{3}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1}{3 ^{2}})^{3} = \frac{1 ^{3}}{( 3 ^{2} ) ^{3}}

= \frac{1}{- \frac{1 ^{3}}{( 3 ^{2} ) ^{3}}}

(3^{2})^{3} : 3^{6}

= \frac{1}{- \frac{1 ^{3}}{3 ^{6}}}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1}{\frac{1 ^{3}}{3 ^{6}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

\frac{1}{\frac{1 ^{3}}{3 ^{6}}} = \frac{3 ^{6}}{1 ^{3}}

= - \frac{3 ^{6}}{1 ^{3}}

Apply rule

1^{a} = 1

1^{3} = 1

= - \frac{3 ^{6}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{3 ^{6}}{1} = 3^{6}

= - 3^{6}

3^{6} = 729

= - 729

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