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Popular >

simplify \sqrt[4]{-625}^3

Solution

simplify

Solution

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

Solution steps

Apply radical rule:

= ((- 625)^{\frac{1}{4}})^{3}

Apply exponent rule:

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

= (- 625)^{\frac{1}{4} \cdot 3}

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

= (- 625)^{\frac{3}{4}}

Apply exponent rule:

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

(- 625)^{\frac{3}{4}} = (- 1)^{\frac{3}{4}} \cdot 62 5^{\frac{3}{4}}

= (- 1)^{\frac{3}{4}} \cdot 62 5^{\frac{3}{4}}

62 5^{\frac{3}{4}} = 125

= 125 (- 1)^{\frac{3}{4}}

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Frequently Asked Questions (FAQ)

What is \sqrt[4]{-625}^3 ?
The solution to \sqrt[4]{-625}^3 is 125(-1)^{3/4}