Solve -28y^7z^2div(-4y^3z^2)

$$- 28 y ^ { 7 } z ^ { 2 } \div ( - 4 y ^ { 3 } z ^ { 2 } )$$

Evaluate

$$7y^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-28\right)^{1}y^{7}z^{2}}{\left(-4\right)^{1}y^{3}z^{2}}$$

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

$$\frac{\left(-28\right)^{1}}{\left(-4\right)^{1}}y^{7-3}z^{2-2}$$

Subtract 3 from 7.

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

Subtract 2 from 2.

$$\frac{\left(-28\right)^{1}}{\left(-4\right)^{1}}y^{4}z^{0}$$

For any number a except 0, a^{0}=1.

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

Divide -28 by -4.

$$7y^{4}$$

Differentiate w.r.t. y

$$28y^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-\frac{28z^{2}}{-4z^{2}}\right)y^{7-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(7y^{4})$$

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}.

$$4\times 7y^{4-1}$$

Do the arithmetic.

$$28y^{3}$$