Solve 1.0*10^3kg/m^3*2.5*10^-3m^3

$$1.0 \times 10 ^ { 3 } kg / m ^ { 3 } \times 2.5 \times 10 ^ { - 3 } m ^ { 3 }$$

Evaluate

$$\frac{5gk}{2}$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$\frac{1\times 1000kg}{m^{3}}\times 2.5\times 10^{-3}m^{3}$$

Multiply 1 and 1000 to get 1000.

$$\frac{1000kg}{m^{3}}\times 2.5\times 10^{-3}m^{3}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{1000kg}{m^{3}}\times 2.5\times \frac{1}{1000}m^{3}$$

Multiply 2.5 and \frac{1}{1000} to get \frac{1}{400}.

$$\frac{1000kg}{m^{3}}\times \frac{1}{400}m^{3}$$

Multiply \frac{1000kg}{m^{3}} times \frac{1}{400} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1000kg}{m^{3}\times 400}m^{3}$$

Cancel out 200 in both numerator and denominator.

$$\frac{5gk}{2m^{3}}m^{3}$$

Express \frac{5gk}{2m^{3}}m^{3} as a single fraction.

$$\frac{5gkm^{3}}{2m^{3}}$$

Cancel out m^{3} in both numerator and denominator.

$$\frac{5gk}{2}$$

Differentiate w.r.t. k

$$\frac{5g}{2}$$