Solve (32x^10y^20)^1/5

$$( 32 x ^ { 10 } y ^ { 20 } ) ^ { 1 / 5 }$$

Evaluate

$$2x^{2}y^{4}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\sqrt[5]{32x^{10}y^{20}}$$

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

$$\sqrt[5]{32}\sqrt[5]{x^{10}}\sqrt[5]{y^{20}}$$

Raise 32 to the power \frac{1}{5}.

$$2\sqrt[5]{x^{10}}\sqrt[5]{y^{20}}$$

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

$$2x^{10\times \frac{1}{5}}y^{20\times \frac{1}{5}}$$

Multiply 10 times \frac{1}{5}.

$$2x^{2}y^{20\times \frac{1}{5}}$$

Multiply 20 times \frac{1}{5}.

$$2x^{2}y^{4}$$

Differentiate w.r.t. x

$$4xy^{4}$$