Solve frac{q^frac{33{4}}}{q^8}

$$\frac { q ^ { \frac { 33 } { 4 } } } { q ^ { 8 } }$$

Evaluate

$$\sqrt[4]{q}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{q^{\frac{33}{4}}}{q^{8}}$$

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

$$q^{\frac{33}{4}-8}$$

Subtract 8 from \frac{33}{4}.

$$\sqrt[4]{q}$$

Differentiate w.r.t. q

$$\frac{1}{4q^{\frac{3}{4}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{1}{1}q^{\frac{33}{4}-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}q}(\sqrt[4]{q})$$

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}.

$$\frac{1}{4}q^{\frac{1}{4}-1}$$

Do the arithmetic.

$$\frac{1}{4}q^{-\frac{3}{4}}$$