Solve (a/s)^-1*b/a=

$$( \frac { a } { s } ) ^ { - 1 } \cdot \frac { b } { a } =$$

Evaluate

$$\frac{bs}{a^{2}}$$

Solution Steps

To raise \frac{a}{s} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{a^{-1}}{s^{-1}}\times \frac{b}{a}$$

Multiply \frac{a^{-1}}{s^{-1}} times \frac{b}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{-1}b}{s^{-1}a}$$

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

$$\frac{b}{\frac{1}{s}a^{2}}$$

Express \frac{1}{s}a^{2} as a single fraction.

$$\frac{b}{\frac{a^{2}}{s}}$$

Divide b by \frac{a^{2}}{s} by multiplying b by the reciprocal of \frac{a^{2}}{s}.

$$\frac{bs}{a^{2}}$$

Differentiate w.r.t. s

$$\frac{b}{a^{2}}$$