Solve a*(-2)^4*(-2)^3=

$$a \cdot ( - 2 ) ^ { 4 } \cdot ( - 2 ) ^ { 3 } =$$

Evaluate

$$-128a$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$a\left(-2\right)^{7}$$

Calculate -2 to the power of 7 and get -128.

$$a\left(-128\right)$$

Differentiate w.r.t. a

$$-128$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\left(-2\right)^{7})$$

Calculate -2 to the power of 7 and get -128.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\left(-128\right))$$

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

$$-128a^{1-1}$$

Subtract 1 from 1.

$$-128a^{0}$$

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

$$-128$$