Solve p^{3}*p^{4}*q^-3*q^3*r^5*r^4

$$p ^ { 3 } \times p ^ { 4 } \times q ^ { - 3 } \times q ^ { 3 } \times r ^ { 5 } \times r ^ { 4 }$$

Evaluate

$$p^{7}r^{9}$$

Steps Using Commutative Property of Multiplication

To multiply powers of the same base, add their exponents.

$$p^{3+4}q^{-3+3}r^{5+4}$$

Add the exponents 3 and 4.

$$p^{7}q^{-3+3}r^{5+4}$$

Add the exponents -3 and 3.

$$p^{7}q^{0}r^{5+4}$$

For any number a except 0, a^{0}=1.

$$p^{7}r^{5+4}$$

Add the exponents 5 and 4.

$$p^{7}r^{9}$$

Differentiate w.r.t. p

$$7p^{6}r^{9}$$