**N-RN.2**, which reads

**Rewrite expressions involving radicals and rational exponents using the properties of exponents.**

There's a lot to consider under this standard, so I'll continue with rational exponents, i.e., *fractions*. What if we wanted to evaluate an expression like this?

We need to recognize that the radical 5 is the same as 5^{1/2}, so

The rules for exponents say to multiply the 1/2 and the 4, giving us 5^{2} or *25*.

We can take this further. Suppose we had

The cube root is the same as 1/3 power. So

We can evaluate 6^{3} as 6 * 6 * 6 = 216.

One more example: How would we handle

The fourth root becomes the 1/4 power.

Now we can get a little fancy with and deal with the multiplication of two fractions:

One final note: The answer doesn't always have to be a rational number. You may exchange one rational power for another, one root for a different one. Consider:

Problems could contain any combination of roots and improper fractions, which may or may not have a simple rational answer. But keep the calculator handy just in case you need to know the sixth root of 117,649. Showing your work, of course.

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