Question

Convert to radical form. Assume variables represent positive real numbers.
5^2/3x^4/3yx^2

∛5x^4yz^2
∛5x^4y^3z^6
∛25x^4y^3z^6
∛25x^4yz^2
none of the answer choices

Answer 1

I can’t be sure what the original exponent expression is from "5^2/3x^4/3yx^2" — that’s ambiguous. Could you retype it using ^ and parentheses, for example 5^(2/3)*x^(4/3)*y^(1/3)*z^(2/3) ?

While you fix that, here are the four answer choices translated into fractional-exponent form (so you can match them to the intended expression):

- ∛(5 x^4 y z^2) = 5^(1/3) x^(4/3) y^(1/3) z^(2/3)
- ∛(5 x^4 y^3 z^6) = 5^(1/3) x^(4/3) y^(1) z^(2)
- ∛(25 x^4 y^3 z^6) = 25^(1/3) x^(4/3) y^(1) z^(2) = 5^(2/3) x^(4/3) y z^2
- ∛(25 x^4 y z^2) = 25^(1/3) x^(4/3) y^(1/3) z^(2/3) = 5^(2/3) x^(4/3) y^(1/3) z^(2/3)

If you tell me the original expression in clear exponent form I’ll pick the correct choice (or show the radical).