Solve frac{28p^{0}q^{4}}{4qp^6r}div21p^-4q^3/r^-1

$$\frac { 28 p ^ { 0 } q ^ { 4 } } { 4 q p ^ { 6 } r } \div \frac { 21 p ^ { - 4 } q ^ { 3 } } { r ^ { - 1 } }$$

Evaluate

$$\frac{1}{3\left(pr\right)^{2}}$$

Solution Steps

Divide \frac{28p^{0}q^{4}}{4qp^{6}r} by \frac{21p^{-4}q^{3}}{r^{-1}} by multiplying \frac{28p^{0}q^{4}}{4qp^{6}r} by the reciprocal of \frac{21p^{-4}q^{3}}{r^{-1}}.

$$\frac{28p^{0}q^{4}r^{-1}}{4qp^{6}r\times 21p^{-4}q^{3}}$$

Cancel out 4\times 7qq^{3} in both numerator and denominator.

$$\frac{\frac{1}{r}p^{0}}{3p^{-4}rp^{6}}$$

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

$$\frac{\frac{1}{r}p^{4}}{3rp^{6}}$$

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

$$\frac{1}{3p^{2}r^{2}}$$

Differentiate w.r.t. p

$$-\frac{2}{3r^{2}p^{3}}$$