Solve (6xy^4)^1/9

$$( 6 x y ^ { 4 } ) ^ { 1 / 9 }$$

Evaluate

$$\sqrt[9]{6x}y^{\frac{4}{9}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\sqrt[9]{6x^{1}y^{4}}$$

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

$$\sqrt[9]{6}\sqrt[9]{x^{1}}\sqrt[9]{y^{4}}$$

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

$$\sqrt[9]{6}\sqrt[9]{x}y^{4\times \frac{1}{9}}$$

Multiply 4 times \frac{1}{9}.

$$\sqrt[9]{6}\sqrt[9]{x}y^{\frac{4}{9}}$$

Differentiate w.r.t. x

$$\frac{\sqrt[9]{6}y^{\frac{4}{9}}}{9x^{\frac{8}{9}}}$$