Solve (z^8)^0z^5

$$( z ^ { 8 } ) ^ { 0 } z ^ { 5 }$$

Evaluate

$$z^{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 8 and 0 to get 0.

$$z^{0}z^{5}$$

To multiply powers of the same base, add their exponents. Add 0 and 5 to get 5.

$$z^{5}$$

Differentiate w.r.t. z

$$5z^{4}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 8 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{0}z^{5})$$

To multiply powers of the same base, add their exponents. Add 0 and 5 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{5})$$

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

$$5z^{5-1}$$

Subtract 1 from 5.

$$5z^{4}$$