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Popular >

simplify \sqrt[4]{4096^3}

Solution

simplify

Solution

512

Solution steps

Apply radical rule:

= (409 6^{3})^{\frac{1}{4}}

Apply exponent rule:

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

= 409 6^{3 \cdot \frac{1}{4}}

3 \cdot \frac{1}{4} = \frac{3}{4}

= 409 6^{\frac{3}{4}}

Factor the number:

4096 = 8^{4}

= (8^{4})^{\frac{3}{4}}

Apply exponent rule:

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

(8^{4})^{\frac{3}{4}} = 8^{4 \cdot \frac{3}{4}} = 8^{3}

= 8^{3}

Refine

= 512

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Frequently Asked Questions (FAQ)

What is \sqrt[4]{4096^3} ?
The solution to \sqrt[4]{4096^3} is 512