[tex]8 {}^{ \frac{2}{3} } \times a - \sqrt[3]{( - 8) {}^{ - 2} } [/tex]

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To simplify the expression, we can first rewrite the terms using exponent rules:

[tex]8 {}^{ \frac{2}{3} } = 8^{ \frac{2}{3} } = (2^3)^{ \frac{2}{3} } = 2^{3 \cdot \frac{2}{3} } = 2^2 = 4[/tex]

Next, we have:

[tex]\sqrt[3]{(-8)^{-2}} = (-8)^{- \frac{2}{3} } = \left( \frac{1}{-8^{2}} \right)^{ \frac{1}{3} } = \left( \frac{1}{64} \right)^{ \frac{1}{3} } = (\frac{1}{4})[/tex]

Substitute these values back into the original expression:

[tex]4 \times a - \frac{1}{4} = 4a - \frac{1}{4}[/tex]

Therefore, the simplified expression is [tex]4a - \frac{1}{4}[/tex].