Solve (3x^2y)^-frac{3{5}}

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

Evaluate

$$\frac{3^{\frac{2}{5}}}{3y^{\frac{3}{5}}x^{\frac{6}{5}}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Raise 3 to the power -\frac{3}{5}.

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

To raise a power to another power, multiply the exponents.

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

Multiply 2 times -\frac{3}{5}.

$$\frac{1}{3^{\frac{3}{5}}}\times \frac{1}{x^{\frac{6}{5}}}y^{-\frac{3}{5}}$$

Differentiate w.r.t. x

$$-\frac{2\times 3^{\frac{2}{5}}}{5y^{\frac{3}{5}}x^{\frac{11}{5}}}$$