Solve 28r^4/-7r^15

$$\frac { 28 r ^ { 4 } } { - 7 r ^ { 15 } }$$

Evaluate

$$-\frac{4}{r^{11}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(28r^{4}\right)^{1}\times \frac{1}{-7r^{15}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$28^{1}\left(r^{4}\right)^{1}\times \frac{1}{-7}\times \frac{1}{r^{15}}$$

Use the Commutative Property of Multiplication.

$$28^{1}\times \frac{1}{-7}\left(r^{4}\right)^{1}\times \frac{1}{r^{15}}$$

To raise a power to another power, multiply the exponents.

$$28^{1}\times \frac{1}{-7}r^{4}r^{15\left(-1\right)}$$

Multiply 15 times -1.

$$28^{1}\times \frac{1}{-7}r^{4}r^{-15}$$

To multiply powers of the same base, add their exponents.

$$28^{1}\times \frac{1}{-7}r^{4-15}$$

Add the exponents 4 and -15.

$$28^{1}\times \frac{1}{-7}r^{-11}$$

Raise 28 to the power 1.

$$28\times \frac{1}{-7}r^{-11}$$

Raise -7 to the power -1.

$$28\left(-\frac{1}{7}\right)r^{-11}$$

Multiply 28 times -\frac{1}{7}.

$$-4r^{-11}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{28^{1}r^{4}}{\left(-7\right)^{1}r^{15}}$$

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

$$\frac{28^{1}r^{4-15}}{\left(-7\right)^{1}}$$

Subtract 15 from 4.

$$\frac{28^{1}r^{-11}}{\left(-7\right)^{1}}$$

Divide 28 by -7.

$$-4r^{-11}$$

Differentiate w.r.t. r

$$\frac{44}{r^{12}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{28}{-7}r^{4-15})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(-4r^{-11})$$

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}.

$$-11\left(-4\right)r^{-11-1}$$

Do the arithmetic.

$$44r^{-12}$$