Final answer:
The expression that is equivalent to ⁵√243 is ⁵√5³.
Step-by-step explanation:
To find the expression that is equivalent to ⁵√243, we need to simplify it using fractional exponents. The fifth root of a number is equivalent to raising the number to the power of 1/5.
Therefore, ⁵√243 can be written as 243^(1/5).
Now, let's simplify each of the given options:
a) ⁵√3⁵ = 3^(5/5) = 3^1 = 3
b) ⁵√2⁵ = 2^(5/5) = 2^1 = 2
c) ⁵√5³ = 5^(3/5)
d) ⁵√9³ = 9^(3/5)
Out of the given options, option c) ⁵√5³ = 5^(3/5) is equivalent to ⁵√243.