Solve -20c^7/-10c^2

$$\frac { - 20 c ^ { 7 } } { - 10 c ^ { 2 } }$$

Evaluate

$$2c^{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-20c^{7}\right)^{1}\times \frac{1}{-10c^{2}}$$

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

$$\left(-20\right)^{1}\left(c^{7}\right)^{1}\times \frac{1}{-10}\times \frac{1}{c^{2}}$$

Use the Commutative Property of Multiplication.

$$\left(-20\right)^{1}\times \frac{1}{-10}\left(c^{7}\right)^{1}\times \frac{1}{c^{2}}$$

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

$$\left(-20\right)^{1}\times \frac{1}{-10}c^{7}c^{2\left(-1\right)}$$

Multiply 2 times -1.

$$\left(-20\right)^{1}\times \frac{1}{-10}c^{7}c^{-2}$$

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

$$\left(-20\right)^{1}\times \frac{1}{-10}c^{7-2}$$

Add the exponents 7 and -2.

$$\left(-20\right)^{1}\times \frac{1}{-10}c^{5}$$

Raise -20 to the power 1.

$$-20\times \frac{1}{-10}c^{5}$$

Raise -10 to the power -1.

$$-20\left(-\frac{1}{10}\right)c^{5}$$

Multiply -20 times -\frac{1}{10}.

$$2c^{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-20\right)^{1}c^{7}}{\left(-10\right)^{1}c^{2}}$$

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

$$\frac{\left(-20\right)^{1}c^{7-2}}{\left(-10\right)^{1}}$$

Subtract 2 from 7.

$$\frac{\left(-20\right)^{1}c^{5}}{\left(-10\right)^{1}}$$

Divide -20 by -10.

$$2c^{5}$$

Differentiate w.r.t. c

$$10c^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\left(-\frac{20}{-10}\right)c^{7-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$10c^{4}$$