Answer:
The equivalent expression to the given expression is [tex]\sqrt[3]{32x^8y^{10}}=2x^2y^3\sqrt[3]{4x^2y}[/tex]
Step-by-step explanation:
The given expression is [tex]\sqrt[3]{32x^8y^{10}}[/tex]
To find the equivalent expression:
[tex]\sqrt[3]{32x^8y^{10}}=(32x^8y^{10})^{\frac{1}{3}}[/tex]
We may write the above expression as below:
[tex]=(32^{\frac{1}{3}})((x^8)^{\frac{1}{3}})((y^{10})^{\frac{1}{3}})[/tex]
[tex]=(2)((4)^{\frac{1}{3}})(x^6)\times (x^2)(x^{\frac{2}{3}})(y^3)(y^{\frac{1}{3}})[/tex] (using square root properties)
[tex]=(2\sqrt[3]{4})(x^2\sqrt[3]{x^2})(y^3\sqrt[3]{y})[/tex] (combining the like terms and doing multiplication )
[tex]=2x^2y^3\sqrt[3]{4x^2y}[/tex]
Therefore [tex]\sqrt[3]{32x^8y^{10}}=2x^2y^3\sqrt[3]{4x^2y}[/tex]
Therefore the equivalent expression to the given expression is [tex]\sqrt[3]{32x^8y^{10}}=2x^2y^3\sqrt[3]{4x^2y}[/tex]
