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Simplify each radical. Assume that all variables represent positive real mumbers. See Example 3 .$$-\sqrt[4]{\frac{81}{x^{4}}}$$

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$-\frac{3}{x}$

Algebra

Chapter 10

Roots, Radicals, and Root Functions

Section 3

Simplifying Radical Expressions

Decimals

Exponents and Polynomials

Equations and Inequalities

Complex Numbers

Missouri State University

Oregon State University

Harvey Mudd College

Baylor University

Lectures

00:44

Simplify each radical. Ass…

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02:51

Express each radical in si…

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So this is the negative. The corporate of 81 over extra fourth, the negatives in front that just stays in front. You can apply the radical of the top and the bottom of the ocean. So you would just say this is the same mass like Robert of 81. Define it by the part of X to the fourth. And when you look at this, we can just say, Oh, what number times itself four times equals anyone and it's actually 33 times three is 93 times 9 27 and 27 times three years. Anyone? So we know that this is gonna be a three, okay? And we know that there's a negative and fun all this I'm gonna bring that never law for right here. So there's the negative. You've got your three on the top and then on the bottom you have four the fourth root of X to the fourth. So remember the crowd route or before through is the same as raising it to explode and one for so you can think of this as X to the fourth raised to the 1/4 right when you raise a power to a power, you multiply the exercise. So what this is really worth is X to the fourth raise, the one for which is actually the floor times one for So let's 404th. Wow. So we can say this is the same as three over X X. The first it's just That's right. Another way to do this is a shortcut is when you're taking the radical of something like this. When you have the four through of extra fourth, you can just take the expert on the variable and divided by the route. So if you have before three direction, Fourth is just the same mass x to the four divided by four, which is what makes it first. So the answer here is negative three or rocks?

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