Question

Need help with this question because I’m pretty sure the answer I checked is wrong

Answer 1

To simplified the expression we need to write the radicand as product of powers that are multiples of three. Let's do that:

`\sqrt[3]{81y^7}=\sqrt[3]{3^3\cdot3\cdot y^6\cdot y}`

Now we grouped the terms in powers we can take the root of:

`\begin{gathered} \sqrt[3]{81y^7}=\sqrt[3]{3^3\cdot3\cdot y^6\cdot y} \\ =\sqrt[3]{(3^3y^6)(3y)} \\ =\sqrt[3]{(3y^2)^3(3y)} \end{gathered}`

Finally we perform the root:

`\begin{gathered} \sqrt[3]{81y^7}=\sqrt[3]{3^3\cdot3\cdot y^6\cdot y} \\ =\sqrt[3]{(3^3y^6)(3y)} \\ =\sqrt[3]{(3y^2)^3(3y)} \\ =3y^2\sqrt[3]{3y} \end{gathered}`

Therefore:

`\sqrt[3]{81y^7}=3y^2\sqrt[3]{3y}`