Solve 16r^3s^-5/4r^-1s^2

$$\frac { 16 r ^ { 3 } s ^ { - 5 } } { 4 r ^ { - 1 } s ^ { 2 } }$$

Evaluate

$$\frac{4r^{4}}{s^{7}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{4s^{-5}r^{3}}{\frac{1}{r}s^{2}}$$

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

$$\frac{4s^{-5}r^{4}}{s^{2}}$$

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

$$\frac{4r^{4}}{s^{7}}$$

Differentiate w.r.t. r

$$\frac{16r^{3}}{s^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{16}{s^{5}\times 4s^{2}}r^{3-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{4}{s^{7}}r^{4})$$

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}.

$$4\times \frac{4}{s^{7}}r^{4-1}$$

Do the arithmetic.

$$\frac{16}{s^{7}}r^{3}$$