Solve frac{-12n^{7}p^5(n^2p^4)}{36nup^7}

$$\frac { - 12 n ^ { 7 } p ^ { 5 } ( n ^ { 2 } p ^ { 4 } ) } { 36 n u p ^ { 7 } }$$

Evaluate

$$-\frac{p^{2}n^{9}}{3\nu }$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$\frac{-12n^{9}p^{5}p^{4}}{36\nu p^{7}}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{-12n^{9}p^{9}}{36\nu p^{7}}$$

Cancel out 12p^{7} in both numerator and denominator.

$$\frac{-p^{2}n^{9}}{3\nu }$$

Cancel out -1 in both numerator and denominator.

$$\frac{p^{2}n^{9}}{-3\nu }$$

Differentiate w.r.t. ν

$$\frac{\left(\frac{p}{\nu }\right)^{2}n^{9}}{3}$$