Final answer:
After simplifying the original expression, √(36a8 / 225a2), it is found to be equivalent to expressions B (StartRoot StartFraction 4 a Superscript 6 Baseline Over 25 EndFraction EndRoot) and E (Two-fifths a cubed) of the given options.
Step-by-step explanation:
To find which expressions are equivalent to √(ø9a8 / 225a2), we'll simplify the original expression and compare it to the provided options:
Simplifying √(ø9a8 / 225a2) gives us:
√(36 / 225) * √(a8 / a2)
√(4/25) * √a6
√(22 / 52) * a3
(2 / 5) * a3
This is equivalent to expression E which states Two-fifths a cubed.
Each other option can be simplified similarly to check for equivalence:
Option A simplifies to (2 / 5) * a4, which is not equivalent.
Option B simplifies to (2 / 5) * a3, which is equivalent.
Option C simplifies to (1 / 5) * a3, which is not equivalent.
Option D simplifies to (2 / 3) * a4, which is not equivalent.
Therefore, the expressions equivalent to the original are options B and E.