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Popular >

simplify \sqrt[8]{50^4}

Solution

simplify

Solution

52

+1

Solution steps

Apply radical rule:

= (5 0^{4})^{\frac{1}{8}}

Apply exponent rule:

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

= 5 0^{4 \cdot \frac{1}{8}}

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

= 5 0^{\frac{1}{2}}

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

= 50

Prime factorization of

50 : 2 \cdot 5^{2}

= 5^{2} \cdot 2

Apply radical rule:

= 2 5^{2}

Apply radical rule:

5^{2} = 5

= 52

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Frequently Asked Questions (FAQ)

What is \sqrt[8]{50^4} ?
The solution to \sqrt[8]{50^4} is 5sqrt(2)