Solve p^{3}qr^2*p^2q^5r*pqr^2

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

Evaluate

$$r^{5}p^{6}q^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$p^{5}qr^{2}q^{5}rpqr^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$p^{6}qr^{2}q^{5}rqr^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$p^{6}q^{6}r^{2}rqr^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$p^{6}q^{7}r^{2}rr^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$p^{6}q^{7}r^{3}r^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$p^{6}q^{7}r^{5}$$

Differentiate w.r.t. p

$$6q^{7}\left(pr\right)^{5}$$