What is ((-5)^{-8})/((-5)^{-3)} ?

The solution to ((-5)^{-8})/((-5)^{-3)} is -1/3125

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simplify ((-5)^{-8})/((-5)^{-3)}

simplify

\frac{( - 5 ) ^{- 8}}{( - 5 ) ^{- 3}}

- \frac{1}{3125}

Decimal Notation

- 0.00032

Solution steps

\frac{( - 5 ) ^{- 8}}{( - 5 ) ^{- 3}}

Apply exponent rule:

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

= (- 5)^{- 8 - (- 3)}

Apply rule

- (- a) = a

= (- 5)^{- 8 + 3}

Add/Subtract the numbers:

- 8 + 3 = - 5

= (- 5)^{- 5}

Apply exponent rule:

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

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

Apply exponent rule:

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

n

is odd

(- 5)^{5} = - 5^{5}

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

Apply the fraction rule:

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

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

5^{5} = 3125

= - \frac{1}{3125}

- 16 t^{2} + 144 = 0

\frac{∣ x - 1 ∣ - x}{1 - ∣ x ∣} \geq 0

16 - x > 9

a^{2} + 7 a + 12

x^{2} - 5 x \geq 0

What is ((-5)^{-8})/((-5)^{-3)} ?
The solution to ((-5)^{-8})/((-5)^{-3)} is -1/3125