Solve (-a)^3*a^0

$$( - a ) ^ { 3 } \times a ^ { 0 }$$

Evaluate

$$-a^{3}$$

Solution Steps

Calculate a to the power of 0 and get 1.

$$\left(-a\right)^{3}\times 1$$

Expand \left(-a\right)^{3}.

$$\left(-1\right)^{3}a^{3}\times 1$$

Calculate -1 to the power of 3 and get -1.

$$-a^{3}$$

Differentiate w.r.t. a

$$-3a^{2}$$

Steps Using Definition of a Derivative

Calculate a to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-a\right)^{3}\times 1)$$

Expand \left(-a\right)^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-1\right)^{3}a^{3}\times 1)$$

Calculate -1 to the power of 3 and get -1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a^{3})$$

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

$$3\left(-1\right)a^{3-1}$$

Multiply 3 times -1.

$$-3a^{3-1}$$

Subtract 1 from 3.

$$-3a^{2}$$