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# Simplifying higher-index root expressions

How to rewrite a radical with variables in it as an exponent and then simplify it using exponent properties. In this example, we simplify ∜(5a⁴b¹²). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What's the difference between a radical and a surd?
• A surd includes only irrational numbers, while a radical can include both rational and irrational numbers.
• based on previous video shouldnt the result be 4^√5|a||b|^3 ? since both a and b can either be positive or negative number...?
• no, ask yourself, if both a and b can be either negative or positive, why should we force it into an absolute and make it only a positive-holding variable? you have to remember variables can hold any number, it's only a representation of what it's supposed to be holding, if a = -1, then we change it by forcing the equation to b positive one, thus the statement is false.
• Just a small quick question, would raising a number to the fourth power be 'hypercubing' in shorthand, like how anything raised to the second power is squared, and raising anything to the third power is cubing. So you know, hypercube is a 4-d cube, so just as ^2 is squaring, and in 2 dimensions, and ^3 is cubing, and in 3 dimensions, maybe ^4 is hypercubing, and in 4 dimensions.
• I suppose, although I've never seen anyone use that. Following your logic, I guess something to the 1st power would be "lining" and something to the 0th power would be... "pointing"? I don't know, it's up to you to decide. Just make sure the person you're talking to knows about "hypercubing" before you use it.
• ok so when i ask questions about what i dont get i know i dont get something i just don,t know what i don,t get do you get it - vampier119
• Yeah I do, but I think if you keep doing the math problem over and over. You'll eventually figure what you don't get or you'll realize what you did wrong and fix it. You just gotta do it a lot to get it sometimes.
• Can the answer also be (ab^3)^4
^4 square root of 5?
• this is so hard i dont get it
• Hey Lizeth,
What specifically are you having trouble with? By the way, don't worry if you're not getting it now. I used to hate math A TON and thanks to several great teachers (and Khan Academy), I now understand a lot of the stuff that I used to hate. Just make sure you keep asking for help whenever you need it. If you keep whacking at it (with the right help from other people), you'll understand it eventually.
• Hi! I am really confused. can somone help me with the quetion that says the square root of 28 by simplyfying each expression because they are all confusing to me. thank you
• 1) Find the prime factorization of 28
28=2*2*7
2) Find the square root of 2*2*7
√2*2*7=2√7