1. The problem is to simplify the expression $100^{-\frac{3}{2}}$ and express the answer with positive exponents. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$. 3. Apply this rule to the expression: $$100^{-\frac{3}{2}} = \frac{1}{100^{\frac{3}{2}}}$$ 4. Next, simplify $100^{\frac{3}{2}}$. Recall that $a^{\frac{m}{n}} = \sqrt[n]{a^m}$. 5. So, $$100^{\frac{3}{2}} = \left(100^{\frac{1}{2}}\right)^3 = (\sqrt{100})^3$$ 6. Since $\sqrt{100} = 10$, we have $$ (10)^3 = 1000 $$ 7. Substitute back: $$\frac{1}{100^{\frac{3}{2}}} = \frac{1}{1000}$$ 8. Therefore, the simplified expression with positive exponents is: $$\boxed{\frac{1}{1000}}$$