Solve -2p^4qr*12p^2qdiv48p^2qr^3

$$- 2 p ^ { 4 } q r \times 12 p ^ { 2 } q \div 48 p ^ { 2 } q r ^ { 3 }$$

Evaluate

$$-\frac{q^{3}r^{4}p^{8}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{-2p^{6}qr\times 12q}{48}p^{2}qr^{3}$$

Multiply q and q to get q^{2}.

$$\frac{-2p^{6}q^{2}r\times 12}{48}p^{2}qr^{3}$$

Multiply -2 and 12 to get -24.

$$\frac{-24p^{6}q^{2}r}{48}p^{2}qr^{3}$$

Divide -24p^{6}q^{2}r by 48 to get -\frac{1}{2}p^{6}q^{2}r.

$$-\frac{1}{2}p^{6}q^{2}rp^{2}qr^{3}$$

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

$$-\frac{1}{2}p^{8}q^{2}rqr^{3}$$

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

$$-\frac{1}{2}p^{8}q^{3}rr^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$-\frac{1}{2}p^{8}q^{3}r^{4}$$

Differentiate w.r.t. r

$$-2p^{8}\left(qr\right)^{3}$$