What is (2^{-5})/((-6)^{-5)} ?

The solution to (2^{-5})/((-6)^{-5)} is -243

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simplify (2^{-5})/((-6)^{-5)}

simplify

\frac{2 ^{- 5}}{( - 6 ) ^{- 5}}

- 243

Solution steps

\frac{2 ^{- 5}}{( - 6 ) ^{- 5}}

Apply exponent rule:

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

\frac{2 ^{- 5}}{( - 6 ) ^{- 5}} = (\frac{2}{- 6})^{- 5}

= (\frac{2}{- 6})^{- 5}

\frac{2}{- 6} = - \frac{1}{3}

= (- \frac{1}{3})^{- 5}

Apply exponent rule:

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

= \frac{1}{( - \frac{1}{3} ) ^{5}}

Apply exponent rule:

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

n

is odd

(- \frac{1}{3})^{5} = - (\frac{1}{3})^{5}

= \frac{1}{- ( \frac{1}{3} ) ^{5}}

Apply exponent rule:

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

(\frac{1}{3})^{5} = \frac{1 ^{5}}{3 ^{5}}

= \frac{1}{- \frac{1 ^{5}}{3 ^{5}}}

Apply the fraction rule:

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

= - \frac{1}{\frac{1 ^{5}}{3 ^{5}}}

Apply the fraction rule:

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

\frac{1}{\frac{1 ^{5}}{3 ^{5}}} = \frac{3 ^{5}}{1 ^{5}}

= - \frac{3 ^{5}}{1 ^{5}}

Apply rule

1^{a} = 1

1^{5} = 1

= - \frac{3 ^{5}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{3 ^{5}}{1} = 3^{5}

= - 3^{5}

3^{5} = 243

= - 243

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