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Popular >

simplify \sqrt[4]{625^3}

Solution

simplify

Solution

125

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

Factor the number:

625 = 5^{4}

= (5^{4})^{\frac{3}{4}}

Apply exponent rule:

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

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

= 5^{3}

Refine

= 125

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Frequently Asked Questions (FAQ)

What is \sqrt[4]{625^3} ?
The solution to \sqrt[4]{625^3} is 125