Solve x(-4)^6*(-4)^5

$$x ( - 4 ) ^ { 6 } \times ( - 4 ) ^ { 5 }$$

Evaluate

$$-4194304x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$x\left(-4\right)^{11}$$

Calculate -4 to the power of 11 and get -4194304.

$$x\left(-4194304\right)$$

Differentiate w.r.t. x

$$-4194304$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\left(-4\right)^{11})$$

Calculate -4 to the power of 11 and get -4194304.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\left(-4194304\right))$$

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

$$-4194304x^{1-1}$$

Subtract 1 from 1.

$$-4194304x^{0}$$

For any term t except 0, t^{0}=1.

$$-4194304$$