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

The solution to ((-1/2)^3)^{-3} is -512

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

simplify

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

- 512

Solution steps

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

Apply exponent rule:

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

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

3 (- 3) = - 9

= (- \frac{1}{2})^{- 9}

Apply exponent rule:

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

= \frac{1}{( - \frac{1}{2} ) ^{9}}

Apply exponent rule:

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

n

is odd

(- \frac{1}{2})^{9} = - (\frac{1}{2})^{9}

= \frac{1}{- ( \frac{1}{2} ) ^{9}}

Apply exponent rule:

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

(\frac{1}{2})^{9} = \frac{1 ^{9}}{2 ^{9}}

= \frac{1}{- \frac{1 ^{9}}{2 ^{9}}}

Apply the fraction rule:

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

= - \frac{1}{\frac{1 ^{9}}{2 ^{9}}}

Apply the fraction rule:

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

\frac{1}{\frac{1 ^{9}}{2 ^{9}}} = \frac{2 ^{9}}{1 ^{9}}

= - \frac{2 ^{9}}{1 ^{9}}

Apply rule

1^{a} = 1

1^{9} = 1

= - \frac{2 ^{9}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{2 ^{9}}{1} = 2^{9}

= - 2^{9}

2^{9} = 512

= - 512

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