In Exercises 21–38, rewrite each expression with rational exponen...

Question

In Exercises 21–38, rewrite each expression with rational exponents.
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Accepted Answer

Hello, today we're gonna be rewriting the following expression using rational exponents or in other words, we're going to be rewriting the given expression without the need of the square root symbol. So what we are given is the cube root of 21. And we have an exponential property that states that if we have the M root of A to the power of N, we can go ahead and rewrite this quantity as A to the power of N over M here, the innermost exponent inside of the square root symbol becomes the numerator for the new rational exponent. And the outermost number in front of the square root symbol becomes the denominator of the rational exponent. So going back to our original expression 21 is raised to the power of one. So we're going to allow N to equal to one in this case. And their outermost number in front of the square root symbol is three. So M is going to equal to three. So if we apply this property to the given expression, we can go ahead and rewrite the expression as the quantity 21 race to the power of 1/3 and this is going to be the simplified form of the given expression using rational exponents. And with that being said, the answer to this problem is going to be b 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 21–38, rewrite each expression with rational exponents. _ ∛5

Key Concepts

Rational Exponents

Radical Notation

Properties of Exponents

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