Solve frac{z^frac{7{4}}}{z^frac{3{4}}}

$$\frac { z ^ { \frac { 7 } { 4 } } } { z ^ { \frac { 3 } { 4 } } }$$

Evaluate

$$z$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{z^{\frac{7}{4}}}{z^{\frac{3}{4}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$z^{\frac{7}{4}-\frac{3}{4}}$$

Subtract \frac{3}{4} from \frac{7}{4} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$z^{1}$$

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

$$z$$

Differentiate w.r.t. z

$$1$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{1}z^{\frac{7}{4}-\frac{3}{4}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{1})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$z^{1-1}$$

Do the arithmetic.

$$z^{0}$$

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

$$1$$