Solve frac{6.7*10^{-11}Nm^{2}kg^2*6*10^24kg*7.4*10^2k}{2.02*10^20N}

$$\frac { 6.7 \times 10 ^ { - 11 } Nm ^ { 2 } kg ^ { 2 } \times 6 \times 10 ^ { 24 } kg \times 7.4 \times 10 ^ { 2 } k } { 2.02 \times 10 ^ { 20 } N }$$

Evaluate

$$\frac{7437m^{2}\left(gk\right)^{3}}{5050000}$$

Solution Steps

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

$$\frac{6.7\times 10^{13}Nm^{2}kg^{2}\times 6kg\times 7.4\times 10^{2}k}{2.02\times 10^{20}N}$$

To multiply powers of the same base, add their exponents. Add 13 and 2 to get 15.

$$\frac{6.7\times 10^{15}Nm^{2}kg^{2}\times 6kg\times 7.4k}{2.02\times 10^{20}N}$$

Multiply k and k to get k^{2}.

$$\frac{6.7\times 10^{15}Nm^{2}k^{2}g^{2}\times 6g\times 7.4k}{2.02\times 10^{20}N}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{6.7\times 10^{15}Nm^{2}k^{3}g^{2}\times 6g\times 7.4}{2.02\times 10^{20}N}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{6.7\times 10^{15}Nm^{2}k^{3}g^{3}\times 6\times 7.4}{2.02\times 10^{20}N}$$

Cancel out 10^{15}N in both numerator and denominator.

$$\frac{6\times 6.7\times 7.4m^{2}g^{3}k^{3}}{2.02\times 10^{5}}$$

Multiply 6 and 6.7 to get 40.2.

$$\frac{40.2\times 7.4m^{2}g^{3}k^{3}}{2.02\times 10^{5}}$$

Multiply 40.2 and 7.4 to get 297.48.

$$\frac{297.48m^{2}g^{3}k^{3}}{2.02\times 10^{5}}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{297.48m^{2}g^{3}k^{3}}{2.02\times 100000}$$

Multiply 2.02 and 100000 to get 202000.

$$\frac{297.48m^{2}g^{3}k^{3}}{202000}$$

Divide 297.48m^{2}g^{3}k^{3} by 202000 to get \frac{7437}{5050000}m^{2}g^{3}k^{3}.

$$\frac{7437}{5050000}m^{2}g^{3}k^{3}$$

Differentiate w.r.t. m

$$\frac{7437m\left(gk\right)^{3}}{2525000}$$