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Popular >

simplify \sqrt[8]{256^7}

Solution

simplify

Solution

128

Solution steps

Apply radical rule:

= (25 6^{7})^{\frac{1}{8}}

Apply exponent rule:

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

= 25 6^{7 \cdot \frac{1}{8}}

7 \cdot \frac{1}{8} = \frac{7}{8}

= 25 6^{\frac{7}{8}}

Factor the number:

256 = 2^{8}

= (2^{8})^{\frac{7}{8}}

Apply exponent rule:

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

(2^{8})^{\frac{7}{8}} = 2^{8 \cdot \frac{7}{8}} = 2^{7}

= 2^{7}

Refine

= 128

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Frequently Asked Questions (FAQ)

What is \sqrt[8]{256^7} ?
The solution to \sqrt[8]{256^7} is 128