Question

Which expression is equivalent??? help!

Answer 1

The equivalent expression for the given expression
`\sqrt[3]{256x^(10)y^(7) }` is

`4x^(3) y^(2)(\sqrt[3]{4xy} )`

Explanation:

Given:

`\sqrt[3]{256x^(10)y^(7) }`

Solution:

We will see first what is Cube rooting.

`\sqrt[3]{x^(3)} = x`

Law of Indices

`(x^(a))^(b)=x^(a* b)\\and\\x^(a)x^(b) = x^(a+b)`

Now, applying above property we get

`\sqrt[3]{256x^(10)y^(7) }=\sqrt[3]{(4^(3)* 4* (x^(3))^(3)* x* (y^(2))^(3)* y   )} \\\\\textrm{Cube Rooting we get}\\\sqrt[3]{256x^(10)y^(7) }= 4* x^(3)* y^(2)(\sqrt[3]{4xy}) \\\\\sqrt[3]{256x^(10)y^(7) }= 4x^(3)y^(2)(\sqrt[3]{4xy})`

∴ The equivalent expression for the given expression
`\sqrt[3]{256x^(10)y^(7) }` is

`4x^(3) y^(2)(\sqrt[3]{4xy} )`