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Popular >

simplify 81^{8^{-9^{-2^{-1}}}}

Solution

simplify

8 1^{8^{- 9^{- 2^{- 1}}}}

Solution

9

Solution steps

8 1^{8^{- 9^{- 2^{- 1}}}}

8^{- 9^{- 2^{- 1}}} = \frac{1}{2}

= 8 1^{\frac{1}{2}}

Factor the number:

81 = 9^{2}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

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

2 \cdot \frac{1}{2} = 1

= 9^{1}

Apply exponent rule:

a^{1} = a

= 9

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Frequently Asked Questions (FAQ)

What is 81^{8^{-9^{-2^{-1}}}} ?
The solution to 81^{8^{-9^{-2^{-1}}}} is 9