Solve sqrt[3]{6.67*10^-11*6*10^24*(24*3600)^2/4*3.14*3.14}

$$\sqrt[ 3 ] { \frac { 6.67 \times 10 ^ { - 11 } \times 6 \times 10 ^ { 24 } \times ( 24 \times 3600 ) ^ { 2 } } { 4 \times 3.14 \times 3.14 } }$$

Evaluate

$$\frac{36000000\sqrt[3]{40020}\times 24649^{\frac{2}{3}}}{24649}\approx 42311825.273216285$$

Solution Steps

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

$$\sqrt[3]{\frac{6.67\times 10^{13}\times 6\times \left(24\times 3600\right)^{2}}{4\times 3.14\times 3.14}}$$

Cancel out 2 in both numerator and denominator.

$$\sqrt[3]{\frac{3\times 6.67\times 10^{13}\times \left(24\times 3600\right)^{2}}{2\times 3.14\times 3.14}}$$

Multiply 3 and 6.67 to get 20.01.

$$\sqrt[3]{\frac{20.01\times 10^{13}\times \left(24\times 3600\right)^{2}}{2\times 3.14\times 3.14}}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\sqrt[3]{\frac{20.01\times 10000000000000\times \left(24\times 3600\right)^{2}}{2\times 3.14\times 3.14}}$$

Multiply 20.01 and 10000000000000 to get 200100000000000.

$$\sqrt[3]{\frac{200100000000000\times \left(24\times 3600\right)^{2}}{2\times 3.14\times 3.14}}$$

Multiply 24 and 3600 to get 86400.

$$\sqrt[3]{\frac{200100000000000\times 86400^{2}}{2\times 3.14\times 3.14}}$$

Calculate 86400 to the power of 2 and get 7464960000.

$$\sqrt[3]{\frac{200100000000000\times 7464960000}{2\times 3.14\times 3.14}}$$

Multiply 200100000000000 and 7464960000 to get 1493738496000000000000000.

$$\sqrt[3]{\frac{1493738496000000000000000}{2\times 3.14\times 3.14}}$$

Multiply 2 and 3.14 to get 6.28.

$$\sqrt[3]{\frac{1493738496000000000000000}{6.28\times 3.14}}$$

Multiply 6.28 and 3.14 to get 19.7192.

$$\sqrt[3]{\frac{1493738496000000000000000}{19.7192}}$$

Expand \frac{1493738496000000000000000}{19.7192} by multiplying both numerator and the denominator by 10000.

$$\sqrt[3]{\frac{14937384960000000000000000000}{197192}}$$

Reduce the fraction \frac{14937384960000000000000000000}{197192} to lowest terms by extracting and canceling out 8.

$$\sqrt[3]{\frac{1867173120000000000000000000}{24649}}$$