Simplify each radical. Assume all variables represent positive re...

Question

Simplify each radical. Assume all variables represent positive real numbers. ⁶√11³

Accepted Answer

Hello. Today we're going to be simplifying the given expression. So what we are given is the 82nd route Of 23 raised to the power of 41. Now the easiest way to simplify this is to go ahead and rewrite the current route into exponential form. There's a rule that allows us to do that. Let's assume that we have the end root of X. To the power of A. If I wanted to rewrite this into an exponential form, I can go ahead and rewrite this as X. To the power of A over N. This is where the innermost exponent becomes the numerator of the new exponent. And the number in front of the route becomes the denominator of the new exponent. So if I apply this rule to the current expression, I can rewrite the the second root of 23 raised to the power of as 23. Race of the power of 41/82. And looking at the current exponent, I can go ahead and reduce 41/82 by dividing both the numerator and denominator by 41. Doing this is gonna allow me to rewrite the exponent as 1/2. So what I have is 23 raised to the power of 1/2. And if I use this exponential rule one more time, I can rewrite 23 raised to the power of 1/2. As the second root of 23 races, the power of one, which is going to be 23. Now, since I have the second root of 23, I don't necessarily need to have this two in front of the square root, so I can just rewrite this as the square root of 23. And this is going to be the simplified form of the current expression. And with that being said, the answer to this problem is going to be a So I hope this video helps you in understanding how to approach this problem, and I'll go ahead and see you all in the next video.

Struggling with College Algebra?

Simplify each radical. Assume all variables represent positive real numbers. ⁶√11³

Watch next

Radical Expressions practice set