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Popular >

simplify \sqrt[4]{(-81)^3}

Solution

simplify

Solution

27 (- 1)^{\frac{3}{4}}

Solution steps

Apply radical rule:

= ((- 81)^{3})^{\frac{1}{4}}

Apply exponent rule:

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

= (- 81)^{3 \cdot \frac{1}{4}}

3 \cdot \frac{1}{4} = \frac{3}{4}

= (- 81)^{\frac{3}{4}}

Apply exponent rule:

(- a)^{\frac{m}{n}} = (- 1)^{\frac{m}{n}} (a)^{\frac{m}{n}}

(- 81)^{\frac{3}{4}} = (- 1)^{\frac{3}{4}} \cdot 8 1^{\frac{3}{4}}

= (- 1)^{\frac{3}{4}} \cdot 8 1^{\frac{3}{4}}

8 1^{\frac{3}{4}} = 27

= 27 (- 1)^{\frac{3}{4}}

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Frequently Asked Questions (FAQ)

What is \sqrt[4]{(-81)^3} ?
The solution to \sqrt[4]{(-81)^3} is 27(-1)^{3/4}