−2197−−−−−√3×−125−−−−√3÷27512−−−−√3=?−21973×−1253÷275123=?\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?" /> −2197−−−−−√3×−125−−−−√3÷27512−−−−√3=?−21973×−1253÷275123=?\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?" /> −2197−−−−−√3×−125−−−−√3÷27512−−−−√3=?−21973×−1253÷275123=?\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?" />

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Simplify : $\sqrt[3]{- 2197} \times \sqrt[3]{- 125} \div \sqrt[3]{\frac{27}{512}} = ?$ $\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?$

1 $\frac{492}{7}$ $\frac{{492}}{7}$
2 $\frac{520}{3}$ $\frac{{520}}{3}$
3 $\frac{554}{7}$ $\frac{{554}}{7}$
4 $\frac{571}{5}$ $\frac{{571}}{5}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} \sqrt[3]{- 2197} \times \sqrt[3]{- 125} \div \sqrt[3]{\frac{27}{512}} \\ = \sqrt[3]{13 \times 13 \times 13 \times - 1} \times \sqrt{5 \times 5 \times 5 \times - 1} \div \sqrt[3]{\frac{27}{512}} \\ = (13 \times 5 \sqrt[3]{- 1 \times - 1}) \div \frac{3}{8} \\ = 13 \times 5 \times \frac{8}{3} \\ = \frac{520}{3} \end{aligned}

$\eqalign{ & \,\,\,\,\,\,\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, \cr & = \root 3 \of {13 \times 13 \times 13 \times - 1} \times \sqrt {5 \times 5 \times 5 \times - 1} \div \root 3 \of {\frac{{27}}{{512}}} \cr & = \left( {13 \times 5\root 3 \of { - 1 \times - 1} } \right) \div \frac{3}{8} \cr & = 13 \times 5 \times \frac{8}{3} \cr & = \frac{{520}}{3} \cr}$

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", "text": "Simplify :

\sqrt[3]{- 2197} \times \sqrt[3]{- 125} \div \sqrt[3]{\frac{27}{512}} = ?

$\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \sqrt[3]{- 2197} \times \sqrt[3]{- 125} \div \sqrt[3]{\frac{27}{512}} \\ = \sqrt[3]{13 \times 13 \times 13 \times - 1} \times \sqrt{5 \times 5 \times 5 \times - 1} \div \sqrt[3]{\frac{27}{512}} \\ = (13 \times 5 \sqrt[3]{- 1 \times - 1}) \div \frac{3}{8} \\ = 13 \times 5 \times \frac{8}{3} \\ = \frac{520}{3} \end{aligned}

$\eqalign{ & \,\,\,\,\,\,\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, \cr & = \root 3 \of {13 \times 13 \times 13 \times - 1} \times \sqrt {5 \times 5 \times 5 \times - 1} \div \root 3 \of {\frac{{27}}{{512}}} \cr & = \left( {13 \times 5\root 3 \of { - 1 \times - 1} } \right) \div \frac{3}{8} \cr & = 13 \times 5 \times \frac{8}{3} \cr & = \frac{{520}}{3} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \sqrt[3]{- 2197} \times \sqrt[3]{- 125} \div \sqrt[3]{\frac{27}{512}} \\ = \sqrt[3]{13 \times 13 \times 13 \times - 1} \times \sqrt{5 \times 5 \times 5 \times - 1} \div \sqrt[3]{\frac{27}{512}} \\ = (13 \times 5 \sqrt[3]{- 1 \times - 1}) \div \frac{3}{8} \\ = 13 \times 5 \times \frac{8}{3} \\ = \frac{520}{3} \end{aligned}

$\eqalign{ & \,\,\,\,\,\,\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, \cr & = \root 3 \of {13 \times 13 \times 13 \times - 1} \times \sqrt {5 \times 5 \times 5 \times - 1} \div \root 3 \of {\frac{{27}}{{512}}} \cr & = \left( {13 \times 5\root 3 \of { - 1 \times - 1} } \right) \div \frac{3}{8} \cr & = 13 \times 5 \times \frac{8}{3} \cr & = \frac{{520}}{3} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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