Solve [a^3/(a^-2)^2*b^7]

$$[ \frac { a ^ { 3 } } { ( a ^ { - 2 } ) ^ { 2 } \cdot b ^ { 7 } } ]$$

Evaluate

$$\left(\frac{a}{b}\right)^{7}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{a^{3}}{a^{-4}b^{7}}$$

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

$$\frac{a^{7}}{b^{7}}$$

Differentiate w.r.t. b

$$-\frac{7a^{7}}{b^{8}}$$