Which expression is equivalent to mc024-1.jpg? mc024-2.jpg mc024-3.jpg mc024-4.jpg mc024-5.jpg

Question

Which expression is equivalent to ?

Answer 1

Answer 2

Breaking the radicand down, let's start with the number 32.

The cubed root of 32 is not an even number, but we can simplify.

What number can we get three of the same of to take out?

32 = 2 • 16

16 = 2 • 8

8 = 2 • 4

We have three 2s so we can take that out from under the radical and place it outside. What's left is 4.

x⁸ is x¹x¹x¹x¹x¹x¹x¹x¹ and we want to take out groups of three (for cubed root) x-variables to get

(x¹x¹x¹)(x¹x¹x¹)x¹x¹

Remember: x¹x¹x¹ = x³

We have TWO groups (x¹x¹x¹) we can take out therefore on the outside we write x² and under the radical we have x¹x¹ which is x^2.

Do the same for y¹⁰ = y¹y¹y¹y¹y¹y¹y¹y¹y¹y¹ how many groups of 3 y-variables can we take out?

(y¹y¹y¹)(y¹y¹y¹)(y¹y¹y¹)y¹

We have THREE groups of (y¹y¹y¹) so we can place y³ outside the radical. What's left is y¹ or simply y

On the outside we have 2, x², y³ and remaining under the radical is 4, x², y

2x²y³ [(4x²y)^1/3] is the answer - the third choice.