Solve (3/ab^2)^-1

$$( \frac { 3 } { a b ^ { 2 } } ) ^ { - 1 }$$

Evaluate

$$\frac{ab^{2}}{3}$$

Solution Steps

To raise \frac{3}{ab^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{3^{-1}}{\left(ab^{2}\right)^{-1}}$$

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

$$\frac{\frac{1}{3}}{\left(ab^{2}\right)^{-1}}$$

Expand \left(ab^{2}\right)^{-1}.

$$\frac{\frac{1}{3}}{a^{-1}\left(b^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\frac{1}{3}}{a^{-1}b^{-2}}$$

Express \frac{\frac{1}{3}}{a^{-1}b^{-2}} as a single fraction.

$$\frac{1}{3a^{-1}b^{-2}}$$

Differentiate w.r.t. a

$$\frac{b^{2}}{3}$$