Solve sqrt[3]{4913}*sqrt[3]{15625}divsqrt[3]{3375/5832}

$$\sqrt[ 3 ] { 4913 } \times \sqrt[ 3 ] { 15625 } \div \sqrt[ 3 ] { \frac { 3375 } { 5832 } }$$

Evaluate

$$510$$

Solution Steps

Calculate \sqrt[3]{4913} and get 17.

$$\frac{17\sqrt[3]{15625}}{\sqrt[3]{\frac{3375}{5832}}}$$

Calculate \sqrt[3]{15625} and get 25.

$$\frac{17\times 25}{\sqrt[3]{\frac{3375}{5832}}}$$

Multiply 17 and 25 to get 425.

$$\frac{425}{\sqrt[3]{\frac{3375}{5832}}}$$

Reduce the fraction \frac{3375}{5832} to lowest terms by extracting and canceling out 27.

$$\frac{425}{\sqrt[3]{\frac{125}{216}}}$$

Calculate \sqrt[3]{\frac{125}{216}} and get \frac{5}{6}.

$$\frac{425}{\frac{5}{6}}$$

Divide 425 by \frac{5}{6} by multiplying 425 by the reciprocal of \frac{5}{6}.

$$425\times \frac{6}{5}$$

Multiply 425 and \frac{6}{5} to get 510.

$$510$$

Factor

$$2\times 3\times 5\times 17$$