Solve (frac{a^{3}b^-5}{a^-3b^5})^-1

$$( \frac { a ^ { 3 } b ^ { - 5 } } { a ^ { - 3 } b ^ { 5 } } ) ^ { - 1 }$$

Evaluate

$$\frac{b^{10}}{a^{6}}$$

Solution Steps

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

$$\left(\frac{b^{-5}a^{6}}{b^{5}}\right)^{-1}$$

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

$$\left(\frac{a^{6}}{b^{10}}\right)^{-1}$$

To raise \frac{a^{6}}{b^{10}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{6}\right)^{-1}}{\left(b^{10}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -1 to get -6.

$$\frac{a^{-6}}{\left(b^{10}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and -1 to get -10.

$$\frac{a^{-6}}{b^{-10}}$$

Differentiate w.r.t. b

$$\frac{10b^{9}}{a^{6}}$$