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Express each radical in simplified form. Assume that all variables represent positive real mumbers. See Example 5$$\sqrt[4]{81 x^{12} y^{16}}$$
$3 x^{3} y^{4}$
Algebra
Chapter 10
Roots, Radicals, and Root Functions
Section 3
Simplifying Radical Expressions
Decimals
Exponents and Polynomials
Equations and Inequalities
Complex Numbers
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J When simplifying this fourth root, what you're gonna end up doing is you're gonna hopefully recognize that 81 to 56 are perfect. Uh, explosive four. Basically, when you have three of the fourth, you get 81 you have for the fourth to get to the sex. So you're gonna separate that 43 to 81 to two sex and see the fourth of 18? Why not, huh? The four through of 2 56 on a Okay. And then you've got the four throughout to you 12 and we're gonna multiply that by the 43 years you'd be a remember the shortcut for working with these exponents of the variables. Just provide the exponent inside by the level of the route radical. So we 12 divided by four for the TV off, which means that the route would be t that the third, because t the third time's itself four times that you well, and you into the eighth for three of that would be second because you knew the second time's itself four times gonna be to the eighth. And over here, we've got the fraction we can work with here. The 43 of 81 is gonna be three. And the fourth row to 36 is gonna before. So ultimately, what we're looking at after we simplify everything is a very simple relationship that is just 3/4 times tt that there have a seat to the second. That's it. That's your simplest form.
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