Solve 8y^7z^6/4y^6z^5

$$\frac { 8 y ^ { 7 } z ^ { 6 } } { 4 y ^ { 6 } z ^ { 5 } }$$

Evaluate

$$2yz$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}y^{7}z^{6}}{4^{1}y^{6}z^{5}}$$

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

$$\frac{8^{1}}{4^{1}}y^{7-6}z^{6-5}$$

Subtract 6 from 7.

$$\frac{8^{1}}{4^{1}}y^{1}z^{6-5}$$

Subtract 5 from 6.

$$\frac{8^{1}}{4^{1}}yz^{1}$$

Divide 8 by 4.

$$2yz$$

Differentiate w.r.t. y

$$2z$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{8z^{6}}{4z^{5}}y^{7-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2zy^{1})$$

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}.

$$2zy^{1-1}$$

Do the arithmetic.

$$2zy^{0}$$

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

$$2z\times 1$$

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

$$2z$$