Solve for x x^(4/3)=81

Problem

x^(4/3)=81

Solution

1. Isolate the variable x by raising both sides of the equation to the reciprocal power of the current exponent, which is 3/4

(x^(4/3))^(3/4)=81^(3/4)

2. Simplify the left side using the power of a power rule, (a^m)^n=a^(m⋅n) which leaves x^1

x=81^(3/4)

3. Rewrite the right side using the definition of rational exponents, a^(m/n)=(√(n,a))^m

x=(√(4,81))^3

4. Evaluate the fourth root of 81 Since 3^4=81 the fourth root is 3

x=3^3

5. Calculate the final value by cubing the result.

x=27

Final Answer

x^(4/3)=81⇒x=27

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