Solve frac{16p^{-3}q^{-2}r^-5}{24p^2q^-4r^-7}

$$\frac { 16 p ^ { - 3 } q ^ { - 2 } r ^ { - 5 } } { 24 p ^ { 2 } q ^ { - 4 } r ^ { - 7 } }$$

Evaluate

$$\frac{2\left(qr\right)^{2}}{3p^{5}}$$

Solution Steps

Cancel out 8 in both numerator and denominator.

$$\frac{2r^{-5}p^{-3}q^{-2}}{3r^{-7}q^{-4}p^{2}}$$

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

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

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

$$\frac{2q^{2}r^{2}}{3p^{5}}$$

Differentiate w.r.t. r

$$\frac{4rq^{2}}{3p^{5}}$$