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I just need someone to show how to brake down and solve this?

I just need someone to show how to brake down and solve this?-example-1

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\begin{gathered} 2\sqrt[]{25y^8}\cdot4\sqrt[]{6y^3}= \\ 8\sqrt[]{25y^8}\cdot\sqrt[]{6y^3}= \\ 8\sqrt[]{25}\cdot\sqrt[]{y^8}\cdot\sqrt[]{6y^3}= \\ 8\cdot5\cdot y^4\cdot\sqrt[]{6y^3}= \\ 40\cdot y^4\cdot\sqrt[]{6y^3}= \\ 40\cdot y^4\cdot\sqrt[]{6y^{}\cdot y^2}= \\ 40\cdot y^4\cdot\sqrt[]{6y^{}}\cdot y= \\ 40\cdot y^5\cdot\sqrt[]{6y^{}}\cdot \end{gathered}
\begin{gathered} \\ \\ \\ \sqrt[]{y^8}=y^{(8)/(2)}=y^4 \end{gathered}

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