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Popular >

simplify 27^{9^{-4^{-2^{-1}}}}

Solution

simplify

2 7^{9^{- 4^{- 2^{- 1}}}}

Solution

3

Solution steps

2 7^{9^{- 4^{- 2^{- 1}}}}

9^{- 4^{- 2^{- 1}}} = \frac{1}{3}

= 2 7^{\frac{1}{3}}

Factor the number:

27 = 3^{3}

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

Apply exponent rule:

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

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

3 \cdot \frac{1}{3} = 1

= 3^{1}

Apply exponent rule:

a^{1} = a

= 3

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Frequently Asked Questions (FAQ)

What is 27^{9^{-4^{-2^{-1}}}} ?
The solution to 27^{9^{-4^{-2^{-1}}}} is 3