Solve 2n^3/3n^2

$$\frac { 2 n ^ { 3 } } { 3 n ^ { 2 } }$$

Evaluate

$$\frac{2n}{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2n^{3}\right)^{1}\times \frac{1}{3n^{2}}$$

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

$$2^{1}\left(n^{3}\right)^{1}\times \frac{1}{3}\times \frac{1}{n^{2}}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times \frac{1}{3}\left(n^{3}\right)^{1}\times \frac{1}{n^{2}}$$

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

$$2^{1}\times \frac{1}{3}n^{3}n^{2\left(-1\right)}$$

Multiply 2 times -1.

$$2^{1}\times \frac{1}{3}n^{3}n^{-2}$$

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

$$2^{1}\times \frac{1}{3}n^{3-2}$$

Add the exponents 3 and -2.

$$2^{1}\times \frac{1}{3}n^{1}$$

Raise 2 to the power 1.

$$2\times \frac{1}{3}n^{1}$$

Multiply 2 times \frac{1}{3}.

$$\frac{2}{3}n^{1}$$

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

$$\frac{2}{3}n$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}n^{3}}{3^{1}n^{2}}$$

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

$$\frac{2^{1}n^{3-2}}{3^{1}}$$

Subtract 2 from 3.

$$\frac{2^{1}n^{1}}{3^{1}}$$

Divide 2 by 3.

$$\frac{2}{3}n^{1}$$

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

$$\frac{2}{3}n$$

Differentiate w.r.t. n

$$\frac{2}{3} = 0.6666666666666666$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{2}{3}n^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{2}{3}n^{1})$$

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}.

$$\frac{2}{3}n^{1-1}$$

Do the arithmetic.

$$\frac{2}{3}n^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{2}{3}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{2}{3}$$