Solve 5p^3q^2/25pq=

$$\frac { 5 p ^ { 3 } q ^ { 2 } } { 25 p q } =$$

Evaluate

$$\frac{qp^{2}}{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{5^{1}p^{3}q^{2}}{25^{1}p^{1}q^{1}}$$

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

$$\frac{5^{1}}{25^{1}}p^{3-1}q^{2-1}$$

Subtract 1 from 3.

$$\frac{5^{1}}{25^{1}}p^{2}q^{2-1}$$

Subtract 1 from 2.

$$\frac{5^{1}}{25^{1}}p^{2}q^{1}$$

Reduce the fraction \frac{5}{25} to lowest terms by extracting and canceling out 5.

$$\frac{1}{5}p^{2}q$$

Differentiate w.r.t. p

$$\frac{2pq}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{5q^{2}}{25q}p^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{q}{5}p^{2})$$

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}.

$$2\times \frac{q}{5}p^{2-1}$$

Do the arithmetic.

$$\frac{2q}{5}p^{1}$$

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

$$\frac{2q}{5}p$$