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Popular >

simplify \sqrt[8]{729^4}

Solution

simplify

Solution

27

Solution steps

Apply radical rule:

= (72 9^{4})^{\frac{1}{8}}

Apply exponent rule:

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

= 72 9^{4 \cdot \frac{1}{8}}

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

= 72 9^{\frac{1}{2}}

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

= 729

Factor the number:

729 = 2 7^{2}

= 2 7^{2}

Apply radical rule:

2 7^{2} = 27

= 27

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Frequently Asked Questions (FAQ)

What is \sqrt[8]{729^4} ?
The solution to \sqrt[8]{729^4} is 27