Question

√6{4096x¹⁵y²⁶}

Explanation:

Step1: Simplify the radical coefficient

First, find the 6th root of 4096. Since $4^6 = 4096$, we have $\sqrt[6]{4096} = 4$.

Step2: Simplify the $x$-term

For $\sqrt[6]{x^{15}}$, use the exponent rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. Calculate $\frac{15}{6}=\frac{5}{2}=2+\frac{1}{2}$, so $\sqrt[6]{x^{15}}=x^2\sqrt[6]{x^3}=x^2\sqrt{x}$.

Step3: Simplify the $y$-term

For $\sqrt[6]{y^{26}}$, use the exponent rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. Calculate $\frac{26}{6}=\frac{13}{3}=4+\frac{1}{3}$, so $\sqrt[6]{y^{26}}=y^4\sqrt[6]{y^2}=y^4\sqrt[3]{y}$.

Step4: Combine all simplified terms

Multiply the results from Steps 1-3 together.

Answer:

$4x^2y^4\sqrt{x}\sqrt[3]{y}$ or written as $4x^2y^4x^{\frac{1}{2}}y^{\frac{1}{3}}=4x^{\frac{5}{2}}y^{\frac{13}{3}}$