Final answer:
To replace the radical sign with a fractional exponent, we express the cube root of x (5∛x) as x raised to the power of 1/3, making it 5x^(1/3).
Step-by-step explanation:
To replace the radical with a fractional exponent, we must understand the relationship between radicals and exponents. The cube root of x, which is written as ∛x, can be expressed as x raised to the power of 1/3. This is because the index of the radical, which is 3 in the case of a cube root, becomes the denominator of the fractional exponent, and the power inside the radical, which is 1 if not specified, becomes the numerator.
Therefore, 5∛x in terms of a fractional exponent is 5x^(1/3).