1. **State the problem:** Simplify the expression $$bc^2 \cdot b^0 c^{-3} \cdot b^{-2} c$$ and express the answer using positive exponents. 2. **Recall exponent rules:** - $a^m \cdot a^n = a^{m+n}$ - $a^0 = 1$ - $a^{-m} = \frac{1}{a^m}$ 3. **Rewrite the expression grouping like bases:** $$b^{1} c^{2} \cdot b^{0} c^{-3} \cdot b^{-2} c^{1}$$ 4. **Combine exponents for $b$:** $$b^{1+0-2} = b^{-1}$$ 5. **Combine exponents for $c$:** $$c^{2 + (-3) + 1} = c^{0}$$ 6. **Simplify $c^{0}$:** $$c^{0} = 1$$ 7. **Final expression:** $$b^{-1} \cdot 1 = b^{-1}$$ 8. **Express with positive exponents:** $$b^{-1} = \frac{1}{b}$$ **Answer:** $$\frac{1}{b}$$