Solve 3w^{3}v^-5uv^7*8u^2*3w^-4

$$3 w ^ { 3 } v ^ { - 5 } u v ^ { 7 } \cdot 8 u ^ { 2 } \cdot 3 w ^ { - 4 }$$

Evaluate

$$\frac{72v^{2}u^{3}}{w}$$

Solution Steps

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

$$3w^{-1}v^{-5}uv^{7}\times 8u^{2}\times 3$$

To multiply powers of the same base, add their exponents. Add -5 and 7 to get 2.

$$3w^{-1}v^{2}u\times 8u^{2}\times 3$$

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

$$3w^{-1}v^{2}u^{3}\times 8\times 3$$

Multiply 3 and 8 to get 24.

$$24w^{-1}v^{2}u^{3}\times 3$$

Multiply 24 and 3 to get 72.

$$72w^{-1}v^{2}u^{3}$$

Differentiate w.r.t. w

$$-72\times \left(\frac{v}{w}\right)^{2}u^{3}$$