Solve 768w^5z^4/36w^2z^2

$$\frac { 768 w ^ { 5 } z ^ { 4 } } { 36 w ^ { 2 } z ^ { 2 } }$$

Evaluate

$$\frac{64z^{2}w^{3}}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{768^{1}w^{5}z^{4}}{36^{1}w^{2}z^{2}}$$

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

$$\frac{768^{1}}{36^{1}}w^{5-2}z^{4-2}$$

Subtract 2 from 5.

$$\frac{768^{1}}{36^{1}}w^{3}z^{4-2}$$

Subtract 2 from 4.

$$\frac{768^{1}}{36^{1}}w^{3}z^{2}$$

Reduce the fraction \frac{768}{36} to lowest terms by extracting and canceling out 12.

$$\frac{64}{3}w^{3}z^{2}$$

Differentiate w.r.t. w

$$64\left(wz\right)^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{768z^{4}}{36z^{2}}w^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{64z^{2}}{3}w^{3})$$

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}.

$$3\times \frac{64z^{2}}{3}w^{3-1}$$

Do the arithmetic.

$$64z^{2}w^{2}$$