Final answer:
The rational exponent 5/3 as a radical is ³√5. The expression (10n)^(3/2) is equivalent to √(10n^3). Lastly, (5x)^(-1/2) as a radical expression is 1/(√5x).
Step-by-step explanation:
To rewrite the rational exponent 5/3 as a radical expression, we break it down into two parts: the denominator tells us the root and the numerator tells us the power.
Therefore, 5/3 as a radical expression would be ³√55, which signifies taking the cube root and then raising it to the power of 5.
However, since we were only asked for the conversion and not to apply the power, the answer is simply b) ³√5.
For the equivalent radical expression for (10n)3/2, we interpret it as the square root of (10n) cubed, which is d) √(10n3).
The expression (5x)-1/2 as a radical expression can be understood as the reciprocal of the square root of 5x, thus the correct answer is d) 1/(√5x).