1. **State the problem:** Evaluate $16^{-1.5}$ without using a calculator. 2. **Recall the formula and rules:** For any positive number $a$ and real number $m$, $a^{-m} = \frac{1}{a^m}$. 3. **Rewrite the exponent:** $16^{-1.5} = 16^{-\frac{3}{2}}$. 4. **Apply the negative exponent rule:** $$16^{-\frac{3}{2}} = \frac{1}{16^{\frac{3}{2}}}$$ 5. **Simplify $16^{\frac{3}{2}}$:** - $16^{\frac{3}{2}} = \left(16^{\frac{1}{2}}\right)^3$ - $16^{\frac{1}{2}}$ is the square root of 16, which is 4. - So, $16^{\frac{3}{2}} = 4^3 = 64$. 6. **Final evaluation:** $$16^{-1.5} = \frac{1}{64}$$ **Answer:** $\boxed{\frac{1}{64}}$ which corresponds to option C.