Solve (-4t^{2})*(2p^2t^3)*(-1/2p^3t^4)

$$( - 4 t ^ { 2 } ) \times ( 2 p ^ { 2 } t ^ { 3 } ) \times ( - \frac { 1 } { 2 } p ^ { 3 } t ^ { 4 } )$$

Evaluate

$$4p^{5}t^{9}$$

Solution Steps

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

$$-4t^{5}\times 2p^{2}\left(-\frac{1}{2}\right)p^{3}t^{4}$$

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

$$-4t^{9}\times 2p^{2}\left(-\frac{1}{2}\right)p^{3}$$

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

$$-4t^{9}\times 2p^{5}\left(-\frac{1}{2}\right)$$

Multiply -4 and 2 to get -8.

$$-8t^{9}p^{5}\left(-\frac{1}{2}\right)$$

Multiply -8 and -\frac{1}{2} to get 4.

$$4t^{9}p^{5}$$

Differentiate w.r.t. p

$$20p^{4}t^{9}$$