Solve (1.5*10^11)(1-0.0167)*sqrt[3]{5.98*10^24/(3)(2.00*10^30)}

$$( 1.5 \times 10 ^ { 11 } ) ( 1 - 0.0167 ) \times \sqrt[ 3 ] { \frac { 5.98 \times 10 ^ { 24 } } { ( 3 ) ( 2.00 \times 10 ^ { 30 } ) } }$$

Evaluate

$$4916500\sqrt[3]{299}\times 300^{\frac{2}{3}}\approx 1473309342.361143351$$

Solution Steps

Calculate 10 to the power of 11 and get 100000000000.

$$1.5\times 100000000000\left(1-0.0167\right)\sqrt[3]{\frac{5.98\times 10^{24}}{3\times 2\times 10^{30}}}$$

Multiply 1.5 and 100000000000 to get 150000000000.

$$150000000000\left(1-0.0167\right)\sqrt[3]{\frac{5.98\times 10^{24}}{3\times 2\times 10^{30}}}$$

Subtract 0.0167 from 1 to get 0.9833.

$$150000000000\times 0.9833\sqrt[3]{\frac{5.98\times 10^{24}}{3\times 2\times 10^{30}}}$$

Multiply 150000000000 and 0.9833 to get 147495000000.

$$147495000000\sqrt[3]{\frac{5.98\times 10^{24}}{3\times 2\times 10^{30}}}$$

Cancel out 10^{24} in both numerator and denominator.

$$147495000000\sqrt[3]{\frac{5.98}{2\times 3\times 10^{6}}}$$

Multiply 2 and 3 to get 6.

$$147495000000\sqrt[3]{\frac{5.98}{6\times 10^{6}}}$$

Calculate 10 to the power of 6 and get 1000000.

$$147495000000\sqrt[3]{\frac{5.98}{6\times 1000000}}$$

Multiply 6 and 1000000 to get 6000000.

$$147495000000\sqrt[3]{\frac{5.98}{6000000}}$$

Expand \frac{5.98}{6000000} by multiplying both numerator and the denominator by 100.

$$147495000000\sqrt[3]{\frac{598}{600000000}}$$

Reduce the fraction \frac{598}{600000000} to lowest terms by extracting and canceling out 2.

$$147495000000\sqrt[3]{\frac{299}{300000000}}$$