Simplify: $\sqrt[3]{343\times (-729)}$

By using the prime factorization method,

$343=7\times 7\times 7=7^3$

$729=9\times 9\times 9=9^3$

Since, $(-729)={(-9)}^3$

Then the value of,

$\sqrt[3]{343\times (-729)}=\sqrt[3]{{\left(7\right)}^3\times {(-9)}^3}$

$\sqrt[3]{343\times (-729)}=7\times -9$

$\sqrt[3]{343\times (-729)}=-63$