1. The problem is to simplify the expression $2^{-3} x^0 (x^2)$. 2. Recall the rules of exponents: - Any number raised to the zero power is 1, so $x^0 = 1$. - When multiplying powers with the same base, add the exponents: $x^a \cdot x^b = x^{a+b}$. - Negative exponents mean reciprocal: $a^{-n} = \frac{1}{a^n}$. 3. Simplify step-by-step: - $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$. - $x^0 = 1$. - So the expression becomes $\frac{1}{8} \times 1 \times x^2 = \frac{x^2}{8}$. 4. Final simplified expression is $$\frac{x^2}{8}$$.