Solve (-a)^3^2

$$( - a ) ^ { 3 ^ { 2 } }$$

Evaluate

$$-a^{9}$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\left(-a\right)^{9}$$

Expand \left(-a\right)^{9}.

$$\left(-1\right)^{9}a^{9}$$

Calculate -1 to the power of 9 and get -1.

$$-a^{9}$$

Differentiate w.r.t. a

$$-9a^{8}$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-a\right)^{9})$$

Expand \left(-a\right)^{9}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-1\right)^{9}a^{9})$$

Calculate -1 to the power of 9 and get -1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a^{9})$$

The derivative of ax^{n} is nax^{n-1}.

$$9\left(-1\right)a^{9-1}$$

Multiply 9 times -1.

$$-9a^{9-1}$$

Subtract 1 from 9.

$$-9a^{8}$$