Solve a^-2b^2/a^2*b^-4

$$\frac { a ^ { - 2 } b ^ { 2 } } { a ^ { 2 } \times b ^ { - 4 } }$$

Evaluate

$$\frac{b^{6}}{a^{4}}$$

Solution Steps

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

$$\frac{a^{-2}b^{6}}{a^{2}}$$

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

$$\frac{b^{6}}{a^{4}}$$

Differentiate w.r.t. a

$$-\frac{4b^{6}}{a^{5}}$$