Question

Which expression is equivalent to...? Screenshots attached. Please help! Thank you.

Answer 1

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

Explanation:

Another complex expression, let's simplify it step by step...

We'll start by re-writing 256 as 4^4

`\sqrt[3]{256 x^(10) y^(7) } = \sqrt[3]{4^(4) x^(10) y^(7) }`

Then we'll extract the 4 from the cubic root. We will then subtract 3 from the exponent (4) to get to a simple 4 inside, and a 4 outside.

`\sqrt[3]{4^(4) x^(10) y^(7) } = 4 \sqrt[3]{4 x^(10) y^(7) }`

Now, we have x^10, so if we divide the exponent by the root factor, we get 10/3 = 3 1/3, which means we will extract x^9 that will become x^3 outside and x will remain inside.

`4 \sqrt[3]{4 x^(10) y^(7) } = 4x^(3) \sqrt[3]{4 x y^(7) }`

For the y's we have y^7 inside the cubic root, that means the true exponent is y^(7/3)... so we can extract y^2 and 1 y will remain inside.

`4x^(3) \sqrt[3]{4 x y^(7) } = 4x^(3) y^(2) \sqrt[3]{4 x y}`

The answer is then:

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