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### Course: Algebra (all content)>Unit 11

Lesson 7: Simplifying radicals (higher-index roots)

# Simplifying cube root expressions

A worked example of simplifying elaborate expressions that contain radicals. In this example, we simplify 5∛(2x²)⋅3∛(4x⁴). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• I'm unclear on why Sal decided to raise everything to the 1/3 power. Couldn't you solve it as is? Or is Sal's way easier? Mystified…
• At he does mention how it works. Sort of.
• so radicals are the same as fraction exponents?
• I think you are right, but you should check with someone else just in case.
• At , How does Sal get know 8^1/3 changes to 2? He didn't really explain that very well, and I'm completely lost.
• Graph the line whose x -intercept is -2 and whose y-intercept is -1
• Hi!
Shouldn't a^x times b^x = (a*b)^ x+x? which in our example is 1/3 + 1/3 instead of just 1/3 power?
A little bit confused. Thanks!
• no, to add the exponents it has to be in the form a^x*a^y and this would equal a^x+y

hope this helped
• , 8 to the 1/3 = 2. This is confusing to me.
• 8^1/3
That's saying what multiplied three times is equal to eight and in this situation it's 2.
2 * 2 * 2 = 8
2^3 = 8^1/3
• So when Sal says it to be 1/3, is it still to the third power?
• I need a video for multiplying with just square roots
• at , when sal raises the 8 to the 1/3, why did he raise it to 1/3 and not 3/1, and do I always have to raise the index over 1?
• A root is the same thing as an exponent to the reciprocal of the degree of the root. So, yes, it must be "over 1"
Thus,
√a = a^(½)
∛a = a^(⅓)
∛(a²) = (a²)^(⅓) = a^(⅔)
∜a = a^(¼)
∜(a³) = (a³)^(¼) = a^(¾)
and so on.
• If you have a fractional exponent in an expression, is it still considered a radical expression even though it doesn't have a root sign?