Solve (-2x^frac{3{3}}y^frac{2{3}})(-4x^frac{4{3}}y^frac{3{3}})

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

Evaluate

$$8y^{\frac{5}{3}}x^{\frac{7}{3}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

To multiply powers of the same base, add their exponents.

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

Add the exponents 1 and \frac{4}{3}.

$$\left(-2\right)^{1}\left(-4\right)^{1}x^{\frac{7}{3}}y^{\frac{2}{3}+1}$$

Add the exponents \frac{2}{3} and 1.

$$\left(-2\right)^{1}\left(-4\right)^{1}x^{\frac{7}{3}}y^{\frac{5}{3}}$$

Multiply -2 times -4.

$$8x^{\frac{7}{3}}y^{\frac{5}{3}}$$

Differentiate w.r.t. x

$$\frac{56x^{\frac{4}{3}}y^{\frac{5}{3}}}{3}$$