Solve 18c^12d^7/9c^7d

$$\frac { 18 c ^ { 12 } d ^ { 7 } } { 9 c ^ { 7 } d }$$

Evaluate

$$2c^{5}d^{6}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{18^{1}c^{12}d^{7}}{9^{1}c^{7}d^{1}}$$

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

$$\frac{18^{1}}{9^{1}}c^{12-7}d^{7-1}$$

Subtract 7 from 12.

$$\frac{18^{1}}{9^{1}}c^{5}d^{7-1}$$

Subtract 1 from 7.

$$\frac{18^{1}}{9^{1}}c^{5}d^{6}$$

Divide 18 by 9.

$$2c^{5}d^{6}$$

Differentiate w.r.t. c

$$10c^{4}d^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{18d^{7}}{9d}c^{12-7})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(2d^{6}c^{5})$$

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}.

$$5\times 2d^{6}c^{5-1}$$

Do the arithmetic.

$$10d^{6}c^{4}$$