Solve (frac{a^{-1}*b^-3}{b^2*a^-2})^-1

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

Evaluate

$$\frac{b^{5}}{a}$$

Solution Steps

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

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

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

$$\left(\frac{a^{1}}{b^{5}}\right)^{-1}$$

Calculate a to the power of 1 and get a.

$$\left(\frac{a}{b^{5}}\right)^{-1}$$

To raise \frac{a}{b^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{a^{-1}}{\left(b^{5}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -1 to get -5.

$$\frac{a^{-1}}{b^{-5}}$$

Differentiate w.r.t. b

$$\frac{5b^{4}}{a}$$