Simplify 1/( cube root of x^4)

Problem

1/√(3,x4)

Solution

1. Rewrite the radical expression in the denominator using a fractional exponent.

√(3,x4)=x4/3

2. Apply the negative exponent rule 1/(an)=a(−n) to move the expression to the numerator.

1/(x4/3)=x(−4/3)

3. Alternative simplification by extracting the perfect cube from the radical.

√(3,x4)=√(3,x3⋅x)=x√(3,x)

4. Rationalize the denominator if required by multiplying the numerator and denominator by √(3,x2)

1/(x√(3,x))⋅√(3,x2)/√(3,x2)=√(3,x2)/(x2)

Final Answer

1/√(3,x4)=x(−4/3)

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