I need help simplifing this radical expression sqrt(24x^6y^11) sqrt is cubed (3) I need to simplify variables in nonnegative real numbers.

can someone help me?

Do you mean this:


( \sqrt { 24x^6 y ^{11}} ) ^ 3


In working with exponents, remember these rules:


a^b \cdot a^ c = a^ {(b + c)} \\
(a^b)^c = a ^{(b \cdot c)}


Taking the square root of something is like raising it to the 1/2 power. So therefore:


\sqrt {x^6} = (x^6)^{ \frac 1 2 } = x^ {(6 \cdot \frac 1 2) } = x^3


and:


( \sqrt {x^6})^3 = ((x^ 6)^{\frac 1 2}) ^ 3 = x^9


Do you see how this works? Now, complete the problem and post back with what you get.

No I am sorry the 3 is in front of the sqrt root.. I do not know how to do math symbols. Its not behind

You mean this then:


\sqrt[3]{24x^6y^{11}}


So rather than taking the square root, you are taking the cube root of whatever is under the square root symbol:


(24x^6y^{11})^ {\frac 1 3 }


Using the principles I outlined in my earlier post, can you take it from here?

for my answer I got 2x^2(2y^11)^1/3

Is this right?

Almost! How did you get that factor of 2 in front of the y?

so there is no 2 its just y^11?

You need to think about that factor of 24 - what is it's cube root? One way to treat it is to change 24 into 8 * 3, and recognize that the cube root of 24 is therefore the cube root of 8 times the cube root of 3. Or:


\sqrt[3] {24 } = 2 \cdot 3 ^ {\small \frac 1 3}


Hope this helps.

Thank you so much for your help. Best to you in all you do.

Deborah