In Exercises 79–112, use rational exponents to simplify each expr...

Question

In Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers.
____
√√x²y

Accepted Answer

Hello, today we're gonna be simplifying the given expression. So what we are given is the square root of the square root of the quantity M N squared. Now, in order to simplify this quantity, we have a property that allows us to simplify a square root inside of a square root. And that property states that if we have the mth root of the nth root of A, then we can go ahead and combine the two square roots together by taking the product of M and N. Or in this case here, we can rewrite it as M times N root of A. So here we have a square root inside of a square root. And since both of the square roots don't have a number in front of them, we can assign the value of two in front of each of the square roots. And so in this case, here, M is going to equal to two and N is going to equal to two. And so we can combine these two square roots together as two times two of the root of M N squared and two times two is going to simplify to give us four. So what we are left with is the fourth root of M N squared. And this is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. ____ √√x²y

Key Concepts

Rational Exponents

Radical Notation

Properties of Exponents

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