According to the Definition of Rational Exponents [part I] , rewrite the radicals as exponents, with your root being your denominator and your index being your numerator. This is when your numerator is 1:

aᵐ\ⁿ = ⁿ√aᵐ

√x → x¹\² → x²\⁴ [Least Common Denominator (LCD)]

⁴√x→ x¹\⁴

Then, according to the Product-to-Power Exponential Rule, whenever you multiply terms with exponents, you add the exponents:

x²\⁴ + x¹\⁴ = x³\⁴

Definition of Radical Exponents [part II (numerator is greater than 1)] → convert back to radical form:

x³\⁴ → ⁴√x³

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3 years ago