Solve c^9/6c^4

$$\frac { c ^ { 9 } } { 6 c ^ { 4 } }$$

Evaluate

$$\frac{c^{5}}{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(c^{1}\right)^{9}\times \frac{1}{6c^{4}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$1^{9}\left(c^{1}\right)^{9}\times \frac{1}{6}\times \frac{1}{c^{4}}$$

Use the Commutative Property of Multiplication.

$$1^{9}\times \frac{1}{6}\left(c^{1}\right)^{9}\times \frac{1}{c^{4}}$$

To raise a power to another power, multiply the exponents.

$$1^{9}\times \frac{1}{6}c^{9}c^{4\left(-1\right)}$$

Multiply 4 times -1.

$$1^{9}\times \frac{1}{6}c^{9}c^{-4}$$

To multiply powers of the same base, add their exponents.

$$1^{9}\times \frac{1}{6}c^{9-4}$$

Add the exponents 9 and -4.

$$1^{9}\times \frac{1}{6}c^{5}$$

Raise 6 to the power -1.

$$\frac{1}{6}c^{5}$$

Differentiate w.r.t. c

$$\frac{5c^{4}}{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{1}{6}c^{9-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{1}{6}c^{5})$$

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}.

$$5\times \frac{1}{6}c^{5-1}$$

Do the arithmetic.

$$\frac{5}{6}c^{4}$$