Solve 1/2z^6*6z^-3=

$$\frac { 1 } { 2 } z ^ { 6 } \cdot 6 z ^ { - 3 } =$$

Evaluate

$$3z^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and -3 to get 3.

$$\frac{1}{2}z^{3}\times 6$$

Multiply \frac{1}{2} and 6 to get 3.

$$3z^{3}$$

Differentiate w.r.t. z

$$9z^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and -3 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{2}z^{3}\times 6)$$

Multiply \frac{1}{2} and 6 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}z}(3z^{3})$$

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

$$3\times 3z^{3-1}$$

Multiply 3 times 3.

$$9z^{3-1}$$

Subtract 1 from 3.

$$9z^{2}$$