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**Method 1**:$x^{\frac{2}{3}} + x^{\frac{1}{3}} -2$ ≤ 0

put x=8

$8^{\frac{2}{3}} + 8^{\frac{1}{3}} -2 =4$

and 4 ≰ 0

Hence,we can eliminate option (2),(4) and (5)

now put x=7

$7^{\frac{2}{3}} + 7^{\frac{1}{3}} -2$ ≰ 0

From here we can eliminate option (3) too.

**Method 2: **$x^{\frac{2}{3}} + x^{\frac{1}{3}} -2$ ≤ 0

we can rewrite this equation as

$(x^{\frac{1}{3}}-1) (x^{\frac{1}{3}}+2)$

-8 ≤ x ≤ 1

Hence,Option(1) **-8 ≤ x ≤ 1 **is the correct choice.