Solve 3v^3/2v^4

$$\frac { 3 v ^ { 3 } } { 2 v ^ { 4 } }$$

Evaluate

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

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3v^{3}\right)^{1}\times \frac{1}{2v^{4}}$$

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

$$3^{1}\left(v^{3}\right)^{1}\times \frac{1}{2}\times \frac{1}{v^{4}}$$

Use the Commutative Property of Multiplication.

$$3^{1}\times \frac{1}{2}\left(v^{3}\right)^{1}\times \frac{1}{v^{4}}$$

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

$$3^{1}\times \frac{1}{2}v^{3}v^{4\left(-1\right)}$$

Multiply 4 times -1.

$$3^{1}\times \frac{1}{2}v^{3}v^{-4}$$

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

$$3^{1}\times \frac{1}{2}v^{3-4}$$

Add the exponents 3 and -4.

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

Raise 3 to the power 1.

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

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

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

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{3^{1}v^{3}}{2^{1}v^{4}}$$

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

$$\frac{3^{1}v^{3-4}}{2^{1}}$$

Subtract 4 from 3.

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

Divide 3 by 2.

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

Differentiate w.r.t. v

$$-\frac{3}{2v^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{3}{2}v^{3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{3}{2}\times \frac{1}{v})$$

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}.

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

Do the arithmetic.

$$-\frac{3}{2}v^{-2}$$