Solve 7r^2t^2/28rt

$$\frac { 7 r ^ { 2 } t ^ { 2 } } { 28 r t }$$

Evaluate

$$\frac{rt}{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{7^{1}r^{2}t^{2}}{28^{1}r^{1}t^{1}}$$

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

$$\frac{7^{1}}{28^{1}}r^{2-1}t^{2-1}$$

Subtract 1 from 2.

$$\frac{7^{1}}{28^{1}}r^{1}t^{2-1}$$

Subtract 1 from 2.

$$\frac{7^{1}}{28^{1}}rt^{1}$$

Reduce the fraction \frac{7}{28} to lowest terms by extracting and canceling out 7.

$$\frac{1}{4}rt$$

Differentiate w.r.t. r

$$\frac{t}{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{7t^{2}}{28t}r^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{t}{4}r^{1})$$

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}.

$$\frac{t}{4}r^{1-1}$$

Do the arithmetic.

$$\frac{t}{4}r^{0}$$

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

$$\frac{t}{4}\times 1$$

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

$$\frac{t}{4}$$