Solve -a^5/(a^2)^3/a^4

$$\frac { \frac { - a ^ { 5 } } { ( a ^ { 2 } ) ^ { 3 } } } { a ^ { 4 } }$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

Express \frac{\frac{-a^{5}}{a^{6}}}{a^{4}} as a single fraction.

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

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{-a^{5}}{a^{10}}$$

Cancel out a^{5} in both numerator and denominator.

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

Differentiate w.r.t. a

$$\frac{5}{a^{6}}$$