Final answer:
The equation requires correcting a typographical error and possibly represents x^(3/2) - 3 = 5. After correcting, we isolate x and raise both sides to the power of 2/3 to find that x = 4, following rules for expressing roots as fractional powers and solving algebraic expressions.
Step-by-step explanation:
The equation given by the student seems to contain a typographical error, but it appears to represent an algebraic equation involving a cube root. The correct interpretation of the equation likely meant to convey would be x^(3/2) - 3 = 5. To solve this equation, we would first isolate the term containing the variable x by adding 3 to both sides to obtain x^(3/2) = 8. We would then take the reciprocal of the fraction in the exponent, in this case, raising both sides of the equation to the power of 2/3 to cancel out the 3/2 exponent on the left side, resulting in x = 8^(2/3).
This process of solving is derived from the general principle that allows us to express roots as fractional powers, for example, x^2 = √x. Applying this rule, 8^(2/3) calculates to 4, because 8^(1/3) or the cube root of 8 equals 2, and 2 squared (2^2) equals 4, thus x = 4.
This would be our solution unless the original equation was not copied correctly, in which case additional clarification would be needed to provide an accurate solution.