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Popular >

simplify \sqrt[8]{25^4}

Solution

simplify

8 2 5^{4}

Solution

5

Solution steps

8 2 5^{4}

Apply radical rule:

n a = a^{\frac{1}{n}}

= (2 5^{4})^{\frac{1}{8}}

Apply exponent rule:

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

= 2 5^{4 \cdot \frac{1}{8}}

4 \cdot \frac{1}{8} = \frac{1}{2}

= 2 5^{\frac{1}{2}}

a^{\frac{1}{2}} = a

= 25

Factor the number:

25 = 5^{2}

= 5^{2}

Apply radical rule:

n a^{n} = a

5^{2} = 5

= 5

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Frequently Asked Questions (FAQ)

What is \sqrt[8]{25^4} ?
The solution to \sqrt[8]{25^4} is 5