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

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

Evaluate

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

Solution Steps

Cancel out 5 in both numerator and denominator.

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

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

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

Calculate 5 to the power of 4 and get 625.

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

Differentiate w.r.t. t

$$1250t^{3}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$1250t^{3}$$