Solve s*s^-1*s^-70/s^-8

$$\frac { s \cdot s ^ { - 1 } \cdot s ^ { - 70 } } { s ^ { - 8 } }$$

Evaluate

$$\frac{1}{s^{62}}$$

Solution Steps

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

$$\frac{s^{-70}}{s^{-8}}$$

Rewrite s^{-8} as s^{-70}s^{62}. Cancel out s^{-70} in both numerator and denominator.

$$\frac{1}{s^{62}}$$

Differentiate w.r.t. s

$$-\frac{62}{s^{63}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{1}{ss^{70}}s^{1-\left(-8\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{1}{s^{71}}s^{9})$$

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}.

$$9\times \frac{1}{s^{71}}s^{9-1}$$

Do the arithmetic.

$$\frac{9}{s^{71}}s^{8}$$