Solve 8c^5/10c^2

$$\frac { 8 c ^ { 5 } } { 10 c ^ { 2 } }$$

Evaluate

$$\frac{4c^{3}}{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8c^{5}\right)^{1}\times \frac{1}{10c^{2}}$$

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

$$8^{1}\left(c^{5}\right)^{1}\times \frac{1}{10}\times \frac{1}{c^{2}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{10}\left(c^{5}\right)^{1}\times \frac{1}{c^{2}}$$

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

$$8^{1}\times \frac{1}{10}c^{5}c^{2\left(-1\right)}$$

Multiply 2 times -1.

$$8^{1}\times \frac{1}{10}c^{5}c^{-2}$$

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

$$8^{1}\times \frac{1}{10}c^{5-2}$$

Add the exponents 5 and -2.

$$8^{1}\times \frac{1}{10}c^{3}$$

Raise 8 to the power 1.

$$8\times \frac{1}{10}c^{3}$$

Multiply 8 times \frac{1}{10}.

$$\frac{4}{5}c^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}c^{5}}{10^{1}c^{2}}$$

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

$$\frac{8^{1}c^{5-2}}{10^{1}}$$

Subtract 2 from 5.

$$\frac{8^{1}c^{3}}{10^{1}}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}c^{3}$$

Differentiate w.r.t. c

$$\frac{12c^{2}}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{8}{10}c^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{4}{5}c^{3})$$

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}.

$$3\times \frac{4}{5}c^{3-1}$$

Do the arithmetic.

$$\frac{12}{5}c^{2}$$