Solve 3*10^8ms^-1/400*10^-9m=

$$\frac { 3 \times 10 ^ { 8 } m s ^ { - 1 } } { 400 \times 10 ^ { - 9 } m } =$$

Evaluate

$$\frac{750000000000000}{s}$$

Solution Steps

Cancel out m in both numerator and denominator.

$$\frac{3\times 10^{8}\times \frac{1}{s}}{400\times 10^{-9}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{3\times 10^{17}\times \frac{1}{s}}{400}$$

Calculate 10 to the power of 17 and get 100000000000000000.

$$\frac{3\times 100000000000000000\times \frac{1}{s}}{400}$$

Multiply 3 and 100000000000000000 to get 300000000000000000.

$$\frac{300000000000000000\times \frac{1}{s}}{400}$$

Express 300000000000000000\times \frac{1}{s} as a single fraction.

$$\frac{\frac{300000000000000000}{s}}{400}$$

Express \frac{\frac{300000000000000000}{s}}{400} as a single fraction.

$$\frac{300000000000000000}{s\times 400}$$

Differentiate w.r.t. s

$$-\frac{750000000000000}{s^{2}}$$