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Popular >

simplify \sqrt[24]{8^{16}}

Solution

simplify

Solution

4

Solution steps

Apply radical rule:

= (8^{16})^{\frac{1}{24}}

Apply exponent rule:

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

= 8^{16 \cdot \frac{1}{24}}

16 \cdot \frac{1}{24} = \frac{2}{3}

= 8^{\frac{2}{3}}

Factor the number:

8 = 2^{3}

= (2^{3})^{\frac{2}{3}}

Apply exponent rule:

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

(2^{3})^{\frac{2}{3}} = 2^{3 \cdot \frac{2}{3}} = 2^{2}

= 2^{2}

Refine

= 4

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Frequently Asked Questions (FAQ)

What is \sqrt[24]{8^{16}} ?
The solution to \sqrt[24]{8^{16}} is 4