Solve {left(2x^4{y}^frac{-4{5}}right)}^4y4/3

$${ \left(2 { x }^{ 4 } { y }^{ \frac{ -4 }{ 5 } } \right) }^{ } 4y \frac{ 4 }{ 3 }$$

Evaluate

$$\frac{32\sqrt[5]{y}x^{4}}{3}$$

Solution Steps

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

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

Calculate 2x^{4}y^{-\frac{4}{5}} to the power of 1 and get 2x^{4}y^{-\frac{4}{5}}.

$$2x^{4}y^{-\frac{4}{5}}\times 4y\times \frac{4}{3}$$

Multiply 2 and 4 to get 8.

$$8x^{4}y^{-\frac{4}{5}}y\times \frac{4}{3}$$

To multiply powers of the same base, add their exponents. Add -\frac{4}{5} and 1 to get \frac{1}{5}.

$$8x^{4}y^{\frac{1}{5}}\times \frac{4}{3}$$

Multiply 8 and \frac{4}{3} to get \frac{32}{3}.

$$\frac{32}{3}x^{4}y^{\frac{1}{5}}$$

Differentiate w.r.t. x

$$\frac{128\sqrt[5]{y}x^{3}}{3}$$