Solve 28*v^3*u^3/24*v^4*u^2

$$\frac { 28 \cdot v ^ { 3 } \cdot u ^ { 3 } } { 24 \cdot v ^ { 4 } \cdot u ^ { 2 } }$$

Evaluate

$$\frac{7u}{6v}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{28^{1}v^{3}u^{3}}{24^{1}v^{4}u^{2}}$$

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

$$\frac{28^{1}}{24^{1}}v^{3-4}u^{3-2}$$

Subtract 4 from 3.

$$\frac{28^{1}}{24^{1}}\times \frac{1}{v}u^{3-2}$$

Subtract 2 from 3.

$$\frac{28^{1}}{24^{1}}\times \frac{1}{v}u^{1}$$

Reduce the fraction \frac{28}{24} to lowest terms by extracting and canceling out 4.

$$\frac{7}{6}\times \frac{1}{v}u$$

Differentiate w.r.t. v

$$-\frac{7u}{6v^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{28u^{3}}{24u^{2}}v^{3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{7u}{6}\times \frac{1}{v})$$

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}.

$$-\frac{7u}{6}v^{-1-1}$$

Do the arithmetic.

$$\left(-\frac{7u}{6}\right)v^{-2}$$