Solve 0.5p^4*2q^2*3p*5/6q^6

$$0.5 p ^ { 4 } \times 2 q ^ { 2 } \times 3 p \times \frac { 5 } { 6 } q ^ { 6 }$$

Evaluate

$$\frac{5p^{5}q^{8}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$0.5p^{5}\times 2q^{2}\times 3\times \frac{5}{6}q^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$0.5p^{5}\times 2q^{8}\times 3\times \frac{5}{6}$$

Multiply 0.5 and 2 to get 1.

$$p^{5}q^{8}\times 3\times \frac{5}{6}$$

Multiply 3 and \frac{5}{6} to get \frac{5}{2}.

$$p^{5}q^{8}\times \frac{5}{2}$$

Differentiate w.r.t. p

$$\frac{25p^{4}q^{8}}{2}$$