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Popular >

simplify \sqrt[3]{(343)^2}

Solution

simplify

Solution

49

Solution steps

Apply radical rule:

= ((343)^{2})^{\frac{1}{3}}

Apply exponent rule:

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

= (343)^{2 \cdot \frac{1}{3}}

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

= (343)^{\frac{2}{3}}

Factor the number:

343 = 7^{3}

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

Apply exponent rule:

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

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

= 7^{2}

Refine

= 49

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{(343)^2} ?
The solution to \sqrt[3]{(343)^2} is 49