Solve 8c^3d^2/4cd^2

$$\frac { 8 c ^ { 3 } d ^ { 2 } } { 4 c d ^ { 2 } }$$

Evaluate

$$2c^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}c^{3}d^{2}}{4^{1}c^{1}d^{2}}$$

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

$$\frac{8^{1}}{4^{1}}c^{3-1}d^{2-2}$$

Subtract 1 from 3.

$$\frac{8^{1}}{4^{1}}c^{2}d^{2-2}$$

Subtract 2 from 2.

$$\frac{8^{1}}{4^{1}}c^{2}d^{0}$$

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

$$\frac{8^{1}}{4^{1}}c^{2}$$

Divide 8 by 4.

$$2c^{2}$$

Differentiate w.r.t. c

$$4c$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{8d^{2}}{4d^{2}}c^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$4c^{1}$$

For any term t, t^{1}=t.

$$4c$$