Solve for x (x+1)^(2/3)=4

Problem

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

Solution

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

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

(x+1)2=64

2. Take the square root of both sides to solve for the base, remembering to include both the positive and negative roots.

√(,(x+1)2)=±√(,64)

x+1=±8

3. Solve for x by subtracting 1 from both sides for both cases.

x=8−1

x=7

x=−8−1

x=−9

4. Verify the solutions by substituting them back into the original equation to ensure they are valid.

(7+1)(2/3)=8(2/3)=(√(3,8))2=2=4

(−9+1)(2/3)=(−8)(2/3)=(√(3,−8))2=(−2)2=4

Final Answer

x=7,−9

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