Solve for x x^(-2/3)=4

Problem

x(−2/3)=4

Solution

1. Rewrite the negative exponent as a reciprocal to clarify the equation.

1/(x(2/3))=4

2. Isolate the term with the variable by taking the reciprocal of both sides.

x(2/3)=1/4

3. Raise both sides of the equation to the power of 3 to eliminate the denominator in the exponent.

(x(2/3))3=(1/4)3

x2=1/64

4. Solve for x by taking the square root of both sides, remembering to include both the positive and negative roots.

x=±√(,1/64)

x=±1/8

5. Verify the solutions in the original equation. Since the exponent −2/3 involves squaring the base (x2 before taking the cube root and reciprocating, both positive and negative values are valid.

Final Answer

x=±1/8

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