Solve 42yz/7y^5z^4

$$\frac { 42 y z } { 7 y ^ { 5 } z ^ { 4 } }$$

Evaluate

$$\frac{6}{z^{3}y^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{42^{1}y^{1}z^{1}}{7^{1}y^{5}z^{4}}$$

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

$$\frac{42^{1}}{7^{1}}y^{1-5}z^{1-4}$$

Subtract 5 from 1.

$$\frac{42^{1}}{7^{1}}y^{-4}z^{1-4}$$

Subtract 4 from 1.

$$\frac{42^{1}}{7^{1}}\times \frac{1}{y^{4}}z^{-3}$$

Divide 42 by 7.

$$6\times \frac{1}{y^{4}}\times \frac{1}{z^{3}}$$

Differentiate w.r.t. z

$$-\frac{18}{\left(yz\right)^{4}}$$