Solve 28y^2/4y^5

$$\frac{ 28 { y }^{ 2 } }{ 4 { y }^{ 5 } }$$

Evaluate

$$\frac{7}{y^{3}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(28y^{2}\right)^{1}\times \frac{1}{4y^{5}}$$

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

$$28^{1}\left(y^{2}\right)^{1}\times \frac{1}{4}\times \frac{1}{y^{5}}$$

Use the Commutative Property of Multiplication.

$$28^{1}\times \frac{1}{4}\left(y^{2}\right)^{1}\times \frac{1}{y^{5}}$$

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

$$28^{1}\times \frac{1}{4}y^{2}y^{5\left(-1\right)}$$

Multiply 5 times -1.

$$28^{1}\times \frac{1}{4}y^{2}y^{-5}$$

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

$$28^{1}\times \frac{1}{4}y^{2-5}$$

Add the exponents 2 and -5.

$$28^{1}\times \frac{1}{4}y^{-3}$$

Raise 28 to the power 1.

$$28\times \frac{1}{4}y^{-3}$$

Multiply 28 times \frac{1}{4}.

$$7y^{-3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{28^{1}y^{2}}{4^{1}y^{5}}$$

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

$$\frac{28^{1}y^{2-5}}{4^{1}}$$

Subtract 5 from 2.

$$\frac{28^{1}y^{-3}}{4^{1}}$$

Divide 28 by 4.

$$7y^{-3}$$

Differentiate w.r.t. y

$$-\frac{21}{y^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{28}{4}y^{2-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(7y^{-3})$$

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}.

$$-3\times 7y^{-3-1}$$

Do the arithmetic.

$$-21y^{-4}$$