Answer:
The equivalent expression for the given expression [tex]\sqrt[3]{256x^{10}y^{7} }[/tex] is
[tex]4x^{3} y^{2}(\sqrt[3]{4xy} )[/tex]
Step-by-step explanation:
Given:
[tex]\sqrt[3]{256x^{10}y^{7} }[/tex]
Solution:
We will see first what is Cube rooting.
[tex]\sqrt[3]{x^{3}} = x[/tex]
Law of Indices
[tex](x^{a})^{b}=x^{a\times b}\\and\\x^{a}x^{b} = x^{a+b}[/tex]
Now, applying above property we get
[tex]\sqrt[3]{256x^{10}y^{7} }=\sqrt[3]{(4^{3}\times 4\times (x^{3})^{3}\times x\times (y^{2})^{3}\times y )} \\\\\textrm{Cube Rooting we get}\\\sqrt[3]{256x^{10}y^{7} }= 4\times x^{3}\times y^{2}(\sqrt[3]{4xy}) \\\\\sqrt[3]{256x^{10}y^{7} }= 4x^{3}y^{2}(\sqrt[3]{4xy})[/tex]
∴ The equivalent expression for the given expression [tex]\sqrt[3]{256x^{10}y^{7} }[/tex] is
[tex]4x^{3} y^{2}(\sqrt[3]{4xy} )[/tex]
