What is 8.6^{-3(-sqrt(2))} ?

The solution to 8.6^{-3(-sqrt(2))} is 9220.21718…

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simplify 8.6^{-3(-sqrt(2))}

simplify

8. 6^{- 3 (- 2)}

9220.21718 \dots

Solution steps

8. 6^{- 3 (- 2)}

Apply exponent rule:

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

= \frac{1}{8. 6 ^{3 (- 2)}}

Remove parentheses:

(- a) = - a

= \frac{1}{8. 6 ^{- 32}}

Apply exponent rule:

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

8. 6^{- 32} = \frac{1}{8. 6 ^{32}}

= \frac{1}{\frac{1}{8. 6 ^{32}}}

Apply the fraction rule:

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

= \frac{8. 6 ^{32}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 8. 6^{32}

8. 6^{32} = 9220.21718 \dots

= 9220.21718 \dots

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