Solve A_2^2A_2^2/A_4^4

$$\frac { A _ { 2 } ^ { 2 } A _ { 2 } ^ { 2 } } { A _ { 4 } ^ { 4 } }$$

Evaluate

$$A_{2}^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{A_{2}^{4}A_{4}^{4}}{A_{4}^{4}}$$

Cancel out A_{4}^{4} in both numerator and denominator.

$$A_{2}^{4}$$

Differentiate w.r.t. A_2

$$4A_{2}^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}A_{2}}(\frac{A_{2}^{4}A_{4}^{4}}{A_{4}^{4}})$$

Cancel out A_{4}^{4} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}A_{2}}(A_{2}^{4})$$

The derivative of ax^{n} is nax^{n-1}.

$$4A_{2}^{4-1}$$

Subtract 1 from 4.

$$4A_{2}^{3}$$