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Popular >

simplify \sqrt[-3]{27^{-4}}

Solution

simplify

Solution

81

Solution steps

Apply radical rule:

= (2 7^{- 4})^{\frac{1}{- 3}}

Apply exponent rule:

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

= 2 7^{(- 4) \frac{1}{- 3}}

(- 4) \frac{1}{- 3} = \frac{4}{3}

= 2 7^{\frac{4}{3}}

Factor the number:

27 = 3^{3}

= (3^{3})^{\frac{4}{3}}

Apply exponent rule:

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

(3^{3})^{\frac{4}{3}} = 3^{3 \cdot \frac{4}{3}} = 3^{4}

= 3^{4}

Refine

= 81

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Frequently Asked Questions (FAQ)

What is \sqrt[-3]{27^{-4}} ?
The solution to \sqrt[-3]{27^{-4}} is 81