Most Majestic Exponent

Step-by-Step Solution

We are solving the equation:

∛(x√3) = x²

Step 1: Write cube root in exponent form

∛(x√3) = (x√3)^1/3

So the equation becomes:

(x√3)^1/3 = x²

Step 2: Eliminate the fractional exponent

Cubing both sides:

((x√3)^1/3)³ = (x²)³

This simplifies to:

x√3 = x⁶

Step 3: Simplify both sides

Divide both sides by x (x ≠ 0):

√3 = x^6-1 = x⁵

Step 4: Solve for x

x⁵ = √3

Taking the 5th root:

x = (√3)^1/5

✅ Final Answer: x = (√3)^1/5

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