Solve 13c^9d^10/26c^9d=

$$\frac { 13 c ^ { 9 } d ^ { 10 } } { 26 c ^ { 9 } d } =$$

Evaluate

$$\frac{d^{9}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{13^{1}c^{9}d^{10}}{26^{1}c^{9}d^{1}}$$

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

$$\frac{13^{1}}{26^{1}}c^{9-9}d^{10-1}$$

Subtract 9 from 9.

$$\frac{13^{1}}{26^{1}}c^{0}d^{10-1}$$

For any number a except 0, a^{0}=1.

$$\frac{13^{1}}{26^{1}}d^{10-1}$$

Subtract 1 from 10.

$$\frac{13^{1}}{26^{1}}d^{9}$$

Reduce the fraction \frac{13}{26} to lowest terms by extracting and canceling out 13.

$$\frac{1}{2}d^{9}$$

Differentiate w.r.t. d

$$\frac{9d^{8}}{2}$$

Steps Using Definition of a Derivative

Cancel out 13dc^{9} in both numerator and denominator.

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

The derivative of ax^{n} is nax^{n-1}.

$$9\times \frac{1}{2}d^{9-1}$$

Multiply 9 times \frac{1}{2}.

$$\frac{9}{2}d^{9-1}$$

Subtract 1 from 9.

$$\frac{9}{2}d^{8}$$