Let's consider each expression for any value of $\(x \neq 0\)$ :
(A) $\(x^{-2}\)$

This equals $\(\frac{1}{x^2}\)$, which is always positive since squaring any nonzero number is positive.
(B) $\(x^0\)$

Any nonzero number to the zero power is 1 , which is positive.
(C) $\(\frac{1}{x^{-3}}\)$

By negative exponent rule, this is $\(\frac{1}{1 / x^3}=x^3\)$. This can be positive or negative depending on the sign of $x$.
(D) $\(|x|\)$

Absolute value is always positive for $\(x \neq 0\)$.
(E) $\(x^{-3} \times x^4\)$

Combine exponents: $\(x^{-3+4}=x^1=x\)$. This can be positive or negative depending on $x$.
(F) $\((x)^4 \times(-x)^4\)$

Both exponents are even powers, so both terms are always positive. Product is positive.
(G) $\(\left(x^{-3}\right)^4\)$
$\(x^{-12}=\frac{1}{x^{12}}\)$. 12th power of any nonzero real is positive, so the result is always positive.

Terms that must be positive (for all $\(x \neq 0\)$ ):
- (A) $\(x^{-2}\)$
- (B) $\(x^0\)$
- (D) $\(|x|\)$
- (F) $\((x)^4 \times(-x)^4\)$
- (G) $\(\left(x^{-3}\right)^4\)$