Solve 28p^5q^4/14p^4q^3

$$\frac { 28 p ^ { 5 } q ^ { 4 } } { 14 p ^ { 4 } q ^ { 3 } }$$

Evaluate

$$2pq$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{28^{1}p^{5}q^{4}}{14^{1}p^{4}q^{3}}$$

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

$$\frac{28^{1}}{14^{1}}p^{5-4}q^{4-3}$$

Subtract 4 from 5.

$$\frac{28^{1}}{14^{1}}p^{1}q^{4-3}$$

Subtract 3 from 4.

$$\frac{28^{1}}{14^{1}}pq^{1}$$

Divide 28 by 14.

$$2pq$$

Differentiate w.r.t. p

$$2q$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{28q^{4}}{14q^{3}}p^{5-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(2qp^{1})$$

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}.

$$2qp^{1-1}$$

Do the arithmetic.

$$2qp^{0}$$

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

$$2q\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2q$$