Solve -9n^3v^2/-6n^2v^6

$$\frac { - 9 n ^ { 3 } v ^ { 2 } } { - 6 n ^ { 2 } v ^ { 6 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-9\right)^{1}n^{3}v^{2}}{\left(-6\right)^{1}n^{2}v^{6}}$$

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

$$\frac{\left(-9\right)^{1}}{\left(-6\right)^{1}}n^{3-2}v^{2-6}$$

Subtract 2 from 3.

$$\frac{\left(-9\right)^{1}}{\left(-6\right)^{1}}n^{1}v^{2-6}$$

Subtract 6 from 2.

$$\frac{\left(-9\right)^{1}}{\left(-6\right)^{1}}nv^{-4}$$

Reduce the fraction \frac{-9}{-6} to lowest terms by extracting and canceling out 3.

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

Differentiate w.r.t. n

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\left(-\frac{9v^{2}}{-6v^{6}}\right)n^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3}{2v^{4}}n^{1})$$

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}.

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

Do the arithmetic.

$$\frac{3}{2v^{4}}n^{0}$$

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

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

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

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