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

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

Evaluate

$$\frac{y^{\frac{11}{3}}}{x^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and -3 to get -5.

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

To multiply powers of the same base, add their exponents. Add 3 and \frac{2}{3} to get \frac{11}{3}.

$$x^{-5}y^{\frac{11}{3}}$$

Differentiate w.r.t. x

$$-\frac{5y^{\frac{11}{3}}}{x^{6}}$$