Solve 5.810^10mleft(1-0.2056right)sqrt[3]{3.310^23kg/210^30kg}

$$5.8 { 10 }^{ 10 } m \left( 1-0.2056 \right) \sqrt[ 3 ]{ \frac{ 3.3 { 10 }^{ 23 } kg }{ 2 { 10 }^{ 30 } kg } }$$

Evaluate

$$9215040\sqrt[3]{33}\times 25^{\frac{2}{3}}m$$

Solution Steps

Calculate 10 to the power of 10 and get 10000000000.

$$5.8\times 10000000000m\left(1-0.2056\right)\sqrt[3]{\frac{3.3\times 10^{23}kg}{2\times 10^{30}kg}}$$

Multiply 5.8 and 10000000000 to get 58000000000.

$$58000000000m\left(1-0.2056\right)\sqrt[3]{\frac{3.3\times 10^{23}kg}{2\times 10^{30}kg}}$$

Subtract 0.2056 from 1 to get 0.7944.

$$58000000000m\times 0.7944\sqrt[3]{\frac{3.3\times 10^{23}kg}{2\times 10^{30}kg}}$$

Multiply 58000000000 and 0.7944 to get 46075200000.

$$46075200000m\sqrt[3]{\frac{3.3\times 10^{23}kg}{2\times 10^{30}kg}}$$

Cancel out 10^{23}gk in both numerator and denominator.

$$46075200000m\sqrt[3]{\frac{3.3}{2\times 10^{7}}}$$

Calculate 10 to the power of 7 and get 10000000.

$$46075200000m\sqrt[3]{\frac{3.3}{2\times 10000000}}$$

Multiply 2 and 10000000 to get 20000000.

$$46075200000m\sqrt[3]{\frac{3.3}{20000000}}$$

Expand \frac{3.3}{20000000} by multiplying both numerator and the denominator by 10.

$$46075200000m\sqrt[3]{\frac{33}{200000000}}$$

Differentiate w.r.t. m

$$9215040\sqrt[3]{33}\times 25^{\frac{2}{3}}$$