Solve 25*E^-4/5^-3*10*E^-8

$$\frac { 25 \times E ^ { - 4 } } { 5 ^ { - 3 } \times 10 \times E ^ { - 8 } }$$

Evaluate

$$\frac{625E^{4}}{2}$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{5E^{-4}}{2\times 5^{-3}E^{-8}}$$

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

$$\frac{5^{4}E^{4}}{2}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{625E^{4}}{2}$$

Differentiate w.r.t. E

$$1250E^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}E}(\frac{25}{\frac{2}{25}}E^{-4-\left(-8\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}E}(\frac{625}{2}E^{4})$$

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}.

$$4\times \frac{625}{2}E^{4-1}$$

Do the arithmetic.

$$1250E^{3}$$