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Express each radical in simplified form. Assume that all variables represent positive real mumbers. See Example 5$$-\sqrt[3]{27 t^{12}}$$
$-3 t^{4}$
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
Harvey Mudd College
Baylor University
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trying to simplify the cube root of fine 70 the 12th. But he used the practical to separate this out. The negative that's in front just tells you that the roots gonna be negative so you can bring a negative upfront. It's fine. Then you have the cube root 27 and we're gonna multiply that by the queue. Grew to 12. Okay, Now the Cuban 27 has a value that's known because the perfect you. So when Jube is 12 cubed is 83 Q just 27. So this means that this is gonna be the negative comes along for the ride. Cuba 27 is three and the Cuban to that's both. That's the same as basically think about it, um, the cube root of t to the fourth times t to the fourth times to the fourth, right? Well, whenever you have a triplicate inside, a few groot used pull that value out right? So that you the fourth times itself three times is to 12. So that means that the cube root of to the 12th is just to the fourth. So our final answer just being negative three t to the fourth. You know, both of those were perfect que factors. Eso We can pull everything out from any secure group
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