Solve -15c^5/3c^8

$$\frac { - 15 c ^ { 5 } } { 3 c ^ { 8 } }$$

Evaluate

$$-\frac{5}{c^{3}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-15c^{5}\right)^{1}\times \frac{1}{3c^{8}}$$

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

$$\left(-15\right)^{1}\left(c^{5}\right)^{1}\times \frac{1}{3}\times \frac{1}{c^{8}}$$

Use the Commutative Property of Multiplication.

$$\left(-15\right)^{1}\times \frac{1}{3}\left(c^{5}\right)^{1}\times \frac{1}{c^{8}}$$

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

$$\left(-15\right)^{1}\times \frac{1}{3}c^{5}c^{8\left(-1\right)}$$

Multiply 8 times -1.

$$\left(-15\right)^{1}\times \frac{1}{3}c^{5}c^{-8}$$

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

$$\left(-15\right)^{1}\times \frac{1}{3}c^{5-8}$$

Add the exponents 5 and -8.

$$\left(-15\right)^{1}\times \frac{1}{3}c^{-3}$$

Raise -15 to the power 1.

$$-15\times \frac{1}{3}c^{-3}$$

Multiply -15 times \frac{1}{3}.

$$-5c^{-3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-15\right)^{1}c^{5}}{3^{1}c^{8}}$$

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

$$\frac{\left(-15\right)^{1}c^{5-8}}{3^{1}}$$

Subtract 8 from 5.

$$\frac{\left(-15\right)^{1}c^{-3}}{3^{1}}$$

Divide -15 by 3.

$$-5c^{-3}$$

Differentiate w.r.t. c

$$\frac{15}{c^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\left(-\frac{15}{3}\right)c^{5-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-5c^{-3})$$

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}.

$$-3\left(-5\right)c^{-3-1}$$

Do the arithmetic.

$$15c^{-4}$$