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

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

Evaluate

$$\frac{\left(\frac{E}{C}\right)^{2}D^{4}}{BA^{3}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 1 to get 2.

$$\frac{A^{-2}BC^{-4}D^{5}}{AB^{2}C^{-2}D}E^{2}$$

Cancel out BD in both numerator and denominator.

$$\frac{C^{-4}A^{-2}D^{4}}{C^{-2}AB}E^{2}$$

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

$$\frac{D^{4}}{BC^{2}A^{3}}E^{2}$$

Express \frac{D^{4}}{BC^{2}A^{3}}E^{2} as a single fraction.

$$\frac{D^{4}E^{2}}{BC^{2}A^{3}}$$

Differentiate w.r.t. B

$$-\frac{\left(\frac{E}{BC}\right)^{2}D^{4}}{A^{3}}$$