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Popular >

simplify \sqrt[8]{256^3}

Solution

simplify

Solution

8

Solution steps

Apply radical rule:

= (25 6^{3})^{\frac{1}{8}}

Apply exponent rule:

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

= 25 6^{3 \cdot \frac{1}{8}}

3 \cdot \frac{1}{8} = \frac{3}{8}

= 25 6^{\frac{3}{8}}

Factor the number:

256 = 2^{8}

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

Apply exponent rule:

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

(2^{8})^{\frac{3}{8}} = 2^{8 \cdot \frac{3}{8}} = 2^{3}

= 2^{3}

Refine

= 8

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Frequently Asked Questions (FAQ)

What is \sqrt[8]{256^3} ?
The solution to \sqrt[8]{256^3} is 8