Solve n^-2/4n^-3

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

Evaluate

$$\frac{n}{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply -3 times -1.

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

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

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

Add the exponents -2 and 3.

$$1^{-2}\times \frac{1}{4}n^{1}$$

Raise 4 to the power -1.

$$\frac{1}{4}n^{1}$$

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

$$\frac{1}{4}n$$

Differentiate w.r.t. n

$$\frac{1}{4} = 0.25$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{4}n^{-2-\left(-3\right)})$$

Do the arithmetic.

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

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}.

$$\frac{1}{4}n^{1-1}$$

Do the arithmetic.

$$\frac{1}{4}n^{0}$$

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

$$\frac{1}{4}\times 1$$

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

$$\frac{1}{4}$$