Solve A^2/A^3

$$\frac { A ^ { 2 } } { A ^ { 3 } }$$

Evaluate

$$\frac{1}{A}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{A^{2}}{A^{3}}$$

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

$$A^{2-3}$$

Subtract 3 from 2.

$$\frac{1}{A}$$

Differentiate w.r.t. A

$$-\frac{1}{A^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}A}(\frac{1}{1}A^{2-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}A}(\frac{1}{A})$$

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}.

$$-A^{-1-1}$$

Do the arithmetic.

$$-A^{-2}$$