Solve frac{a^{3}(b^2)^5}{a^2b^12}

$$\frac { a ^ { 3 } ( b ^ { 2 } ) ^ { 5 } } { a ^ { 2 } b ^ { 12 } }$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{a^{3}b^{10}}{a^{2}b^{12}}$$

Cancel out a^{2}b^{10} in both numerator and denominator.

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

Differentiate w.r.t. b

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