Question
Express (2y)^2/3 in radical form.
Answers
GPT 3.5
To express (2y)^2/3 in radical form, first we can rewrite it as (2y)^(2/3).
Now, apply the power rule for radicals which states that for any real number a and positive integer n:
(a^n)^(1/n) = a
Therefore, (2y)^(2/3) can be expressed as the cube root of (2y)^2:
= ∛((2y)^2)
= ∛(4y^2)
So, (2y)^2/3 in radical form is ∛(4y^2).
Now, apply the power rule for radicals which states that for any real number a and positive integer n:
(a^n)^(1/n) = a
Therefore, (2y)^(2/3) can be expressed as the cube root of (2y)^2:
= ∛((2y)^2)
= ∛(4y^2)
So, (2y)^2/3 in radical form is ∛(4y^2).