Solve 27v^2w/18v^3w

$$\frac { 27 v ^ { 2 } w } { 18 v ^ { 3 } w }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{27^{1}v^{2}w^{1}}{18^{1}v^{3}w^{1}}$$

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

$$\frac{27^{1}}{18^{1}}v^{2-3}w^{1-1}$$

Subtract 3 from 2.

$$\frac{27^{1}}{18^{1}}\times \frac{1}{v}w^{1-1}$$

Subtract 1 from 1.

$$\frac{27^{1}}{18^{1}}\times \frac{1}{v}w^{0}$$

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

$$\frac{27^{1}}{18^{1}}\times \frac{1}{v}$$

Reduce the fraction \frac{27}{18} to lowest terms by extracting and canceling out 9.

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

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.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{27w}{18w}v^{2-3})$$

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.

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