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

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

Evaluate

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

Solution Steps

Cancel out 4 in both numerator and denominator.

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

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

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

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

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

Differentiate w.r.t. r

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

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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