Solve 11w^12z^5/22w^3z^3

$$\frac { 11 w ^ { 12 } z ^ { 5 } } { 22 w ^ { 3 } z ^ { 3 } }$$

Evaluate

$$\frac{z^{2}w^{9}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{11^{1}w^{12}z^{5}}{22^{1}w^{3}z^{3}}$$

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

$$\frac{11^{1}}{22^{1}}w^{12-3}z^{5-3}$$

Subtract 3 from 12.

$$\frac{11^{1}}{22^{1}}w^{9}z^{5-3}$$

Subtract 3 from 5.

$$\frac{11^{1}}{22^{1}}w^{9}z^{2}$$

Reduce the fraction \frac{11}{22} to lowest terms by extracting and canceling out 11.

$$\frac{1}{2}w^{9}z^{2}$$

Differentiate w.r.t. w

$$\frac{9z^{2}w^{8}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{11z^{5}}{22z^{3}}w^{12-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{z^{2}}{2}w^{9})$$

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}.

$$9\times \frac{z^{2}}{2}w^{9-1}$$

Do the arithmetic.

$$\frac{9z^{2}}{2}w^{8}$$