Solve frac{2u^{2}v^2*2u^2v^-4}{v^2}

$$\frac { 2 u ^ { 2 } v ^ { 2 } \cdot 2 u ^ { 2 } v ^ { - 4 } } { v ^ { 2 } }$$

Evaluate

$$4\times \left(\frac{u}{v}\right)^{4}$$

Solution Steps

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

$$\frac{2u^{4}v^{2}\times 2v^{-4}}{v^{2}}$$

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

$$\frac{2u^{4}v^{-2}\times 2}{v^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{2\times 2u^{4}}{v^{4}}$$

Multiply 2 and 2 to get 4.

$$\frac{4u^{4}}{v^{4}}$$

Differentiate w.r.t. u

$$\frac{16u^{3}}{v^{4}}$$