Solve frac{A^{-2}BC^{-4}D^5E}{A^2C^-2D}E^-1

$$\frac { A ^ { - 2 } B C ^ { - 4 } D ^ { 5 } E } { A ^ { 2 } C ^ { - 2 } D } E ^ { - 1 }$$

Evaluate

$$\frac{\left(\frac{D}{A}\right)^{4}B}{C^{2}}$$

Solution Steps

Cancel out D in both numerator and denominator.

$$\frac{C^{-4}A^{-2}BED^{4}}{C^{-2}A^{2}}E^{-1}$$

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

$$\frac{BED^{4}}{C^{2}A^{4}}E^{-1}$$

Express \frac{BED^{4}}{C^{2}A^{4}}E^{-1} as a single fraction.

$$\frac{BED^{4}E^{-1}}{C^{2}A^{4}}$$

Multiply E and E^{-1} to get 1.

$$\frac{BD^{4}}{C^{2}A^{4}}$$

Differentiate w.r.t. B

$$\frac{\left(\frac{D}{A}\right)^{4}}{C^{2}}$$