Solve sqrt[3]{667*10^-11*60*10^24*86400^2/4*(314)^2}

$$\sqrt[ 3 ] { \frac { 667 \times 10 ^ { - 11 } \times 60 \times 10 ^ { 24 } \times 86400 ^ { 2 } } { 4 \times ( 314 ) ^ { 2 } } }$$

Evaluate

$$\frac{36000000\sqrt[3]{4002}\times 24649^{\frac{2}{3}}}{24649}\approx 19639409.571793571$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 24 to get 13.

$$\sqrt[3]{\frac{667\times 10^{13}\times 60\times 86400^{2}}{4\times 314^{2}}}$$

Cancel out 4 in both numerator and denominator.

$$\sqrt[3]{\frac{15\times 667\times 10^{13}\times 86400^{2}}{314^{2}}}$$

Multiply 15 and 667 to get 10005.

$$\sqrt[3]{\frac{10005\times 10^{13}\times 86400^{2}}{314^{2}}}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\sqrt[3]{\frac{10005\times 10000000000000\times 86400^{2}}{314^{2}}}$$

Multiply 10005 and 10000000000000 to get 100050000000000000.

$$\sqrt[3]{\frac{100050000000000000\times 86400^{2}}{314^{2}}}$$

Calculate 86400 to the power of 2 and get 7464960000.

$$\sqrt[3]{\frac{100050000000000000\times 7464960000}{314^{2}}}$$

Multiply 100050000000000000 and 7464960000 to get 746869248000000000000000000.

$$\sqrt[3]{\frac{746869248000000000000000000}{314^{2}}}$$

Calculate 314 to the power of 2 and get 98596.

$$\sqrt[3]{\frac{746869248000000000000000000}{98596}}$$

Reduce the fraction \frac{746869248000000000000000000}{98596} to lowest terms by extracting and canceling out 4.

$$\sqrt[3]{\frac{186717312000000000000000000}{24649}}$$