When simplifying, you should always be on the lookout for like terms. While it might not look like there are like terms in , there are -- we just have to be able to rewrite it to see.

Before we start combining terms, though, let's look a little more closely at this part:

We need to "distribute" that exponent to everything in the parentheses, like so:

But 4 to the one-half power is just the square root of 4, or 2.

Okay, now let's see our equation.

We need to start combining like terms. Take the terms that include x to the one-half power first.

Now take the terms that have x to the one-third power.

All that's left is to write them in order of descending exponents, then convert the fractional exponents into radicals (since that's what our answer choices look like).

When adding and subtracting radicals, make the sure radicand or inside the square root are the same.

If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated.

Since they are the same, just add the numbers in front of the radical:  which is 

Therefore, our final answer is the sum of the integers and the radical:

When adding and subtracting radicals, make the sure radicand or inside the square root are the same.

If they are the same, just add the numbers in front of the radical.

If they are not the same, the answer is just the problem stated.

Since they are the same, just add and subtract the numbers in front:  which is 

Therefore, the final answer will be this sum and the radical added to the end:

The radicals given are not in like-terms.  To simplify, take the common factors for each of the radicals and separate the radicals.  A radical times itself will eliminate the square root sign.

Now that each radical is in its like term, we can now combine like-terms.

We can solve this by simplifying the radicals first: 

Plugging this into the equation gives us: 

First, simplify  to .

Then set up the multiplication problem:

 .

Multiply the terms outside of the radical, then the terms under the radical:

  then simplfy:  

The radical is still not in its simplest form and must be reduced further: 

. This is the radical in its simplest form. 

To solve this, you must remember the rules for simplifying roots. In order to pull something out from the inside, you msut have the amount indicated in the index. Thus, in this case, to pull one x out, you need 3 inside. Thus,

To simplify radicals, you must have common numbers on the inside of the square root. Don't be fooled. There is no way to simplify any of these, so your answer is simply:

Observe that 250 and 150 factor into  and  respectively. So,