Solve (z^frac{8{7}}divz^frac{1{2}})divz^frac{2{7}}

$$( z ^ { \frac { 8 } { 7 } } \div z ^ { \frac { 1 } { 2 } } ) \div z ^ { \frac { 2 } { 7 } }$$

Evaluate

$$z^{\frac{5}{14}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{1}{2} from \frac{8}{7} to get \frac{9}{14}.

$$\frac{z^{\frac{9}{14}}}{z^{\frac{2}{7}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{2}{7} from \frac{9}{14} to get \frac{5}{14}.

$$z^{\frac{5}{14}}$$

Differentiate w.r.t. z

$$\frac{5}{14z^{\frac{9}{14}}}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{1}{2} from \frac{8}{7} to get \frac{9}{14}.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z^{\frac{9}{14}}}{z^{\frac{2}{7}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{2}{7} from \frac{9}{14} to get \frac{5}{14}.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{\frac{5}{14}})$$

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

$$\frac{5}{14}z^{\frac{5}{14}-1}$$

Subtract 1 from \frac{5}{14}.

$$\frac{5}{14}z^{-\frac{9}{14}}$$