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Popular >

simplify \sqrt[7]{128^3}

Solution

simplify

Solution

8

Solution steps

Apply radical rule:

= (12 8^{3})^{\frac{1}{7}}

Apply exponent rule:

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

= 12 8^{3 \cdot \frac{1}{7}}

3 \cdot \frac{1}{7} = \frac{3}{7}

= 12 8^{\frac{3}{7}}

Factor the number:

128 = 2^{7}

= (2^{7})^{\frac{3}{7}}

Apply exponent rule:

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

(2^{7})^{\frac{3}{7}} = 2^{7 \cdot \frac{3}{7}} = 2^{3}

= 2^{3}

Refine

= 8

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Frequently Asked Questions (FAQ)

What is \sqrt[7]{128^3} ?
The solution to \sqrt[7]{128^3} is 8