Simplify by taking roots of the numerator and the demoninator. Assume that all expressions under radicals represent positive numbers.
The square root of 243x^6/y^20 to the fifth root.
Here is what I have so far: the square root of 243x^6 to the fifth root divided by the square root of 4^20 to the fifth root.
This is the answer that I got but I'm sure it is wrong.
3x^4 x^2 to the fifth root divided by y^4.
4^20 is actually suppose to be y^20. Sorry for thr typo.
I redid the problem and got the answer.
To simplify the expression involving taking roots of the numerator and denominator, we need to follow these steps:
Step 1: Simplify the numerator:
First, let's take the square root of 243x^6 to the fifth root. We can break it down as follows:
∛(243x^6) = ∛(81x^6) * ∛3 = (3x^2) * ∛3 = 3x^2∛3
Step 2: Simplify the denominator:
Next, let's take the square root of y^20 to the fifth root.
∛(y^20) = ∛(y^(4*5)) = ∛(y^4) * ∛(y^4) * ∛(y^4) * ∛(y^4) * ∛(y^4) = y^4
Step 3: Final Simplification:
Now, we have the simplified expression:
(3x^2∛3) / y^4
So, your final answer is:
(3x^2∛3) / y^4