Exponent Simplification C387A4

1. **State the problem:** Simplify the expression $$(2^x)^{-6} (8^x)$$. 2. **Recall the exponent rules:** - Power of a power: $$(a^m)^n = a^{mn}$$ - Product of powers with the same base: $$a^m \cdot a^n = a^{m+n}$$ - Express numbers as powers of the same base if possible. 3. **Rewrite each term:** - $$(2^x)^{-6} = 2^{x \cdot (-6)} = 2^{-6x}$$ - Note that $$8 = 2^3$$, so $$8^x = (2^3)^x = 2^{3x}$$ 4. **Multiply the terms:** $$2^{-6x} \cdot 2^{3x} = 2^{-6x + 3x} = 2^{-3x}$$ 5. **Final answer:** The expression simplifies to $$2^{-3x}$$, which corresponds to option A. **Answer:** A. $2^{-3x}$