In Exercises 39–64, rationalize each denominator.

5
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⁴√x

Question

In Exercises 39–64, rationalize each denominator.

5
-------
⁴√x

Accepted Answer

Hello, everyone. We've been asked to eliminate the radical and the denominator by rationalizing the expression we're given is eight over the fourth route of P. We have four answer choices. None of which have a radical in the denominator any longer. And all of which have a different combination of exponents. So let's see which one fits again. We have eight over the fourth route of P to be able to get the fourth root out of the denominator. We are gonna need to multiply the numerator and the denominator by the fourth route of some value to decide what that value is. We need to first rewrite the fourth route. And then we want to figure out what do we need to multiply P by to get P to the fourth power. Remember when you have exponents, when you multiply you add your exponents. So currently P is raised to the first power. So to get this to be P raised to the fourth power, we need to multiply numerator and denominator by P raised to the third power. So we're gonna multiply both by the fourth root of P cubed. So in doing so multiplying straight across the numerator I have eight multiplied by the fourth root of P cubed. And I'm going to rewrite that as eight multiplied by the fourth root of P cubed next to each other. In the denominator. Recall that when you multiply values under a radical that you multiply them as if the radical was not there. So we're rewriting the fourth route and then P to the first multiplied by P to the third will give us P raised to the fourth power. This is exactly what we want in our denominator because now the fourth route and the fourth power will cancel out. So our numerator will remain eight multiplied by the fourth root of P cubed in our denominator. The fourth route of P raised, the fourth is P. There's nothing I can simplify between the numerator and the denominator. So this should be my solution eight multiplied by the fourth root of P cubed over P. And that's answer choice. A have a nice day.

In Exercises 39–64, rationalize each denominator. 5 ------- ⁴√x

Key Concepts

Rationalizing the Denominator

Radicals and Exponents

Multiplying by the Conjugate

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