Question

assuming x and y are both positive, write the following expression in simplest radical form. \\(\sqrt{4x^7y^7}\\)

Explanation:

Step1: Split radical into factors

$\sqrt{4x^7y^7} = \sqrt{4} \cdot \sqrt{x^7} \cdot \sqrt{y^7}$

Step2: Simplify perfect square factor

$\sqrt{4} = 2$

Step3: Rewrite exponents for radicals

$\sqrt{x^7} = \sqrt{x^6 \cdot x} = x^3\sqrt{x}$, $\sqrt{y^7} = \sqrt{y^6 \cdot y} = y^3\sqrt{y}$

Step4: Combine all simplified terms

$2 \cdot x^3\sqrt{x} \cdot y^3\sqrt{y} = 2x^3y^3\sqrt{xy}$

Answer:

$2x^3y^3\sqrt{xy}$