1. **State the problem:** Simplify the expression $$\left(\frac{a^7 b^6}{a^2 b}\right)^4$$ and write the answer using only positive exponents. 2. **Apply the quotient rule for exponents:** When dividing like bases, subtract the exponents: $$\frac{a^7}{a^2} = a^{7-2} = a^5$$ $$\frac{b^6}{b} = b^{6-1} = b^5$$ So inside the parentheses, the expression simplifies to: $$a^5 b^5$$ 3. **Rewrite the expression:** $$\left(a^5 b^5\right)^4$$ 4. **Apply the power of a product rule:** When raising a product to a power, raise each factor to that power: $$a^{5 \times 4} b^{5 \times 4} = a^{20} b^{20}$$ 5. **Final answer:** $$a^{20} b^{20}$$ This is the simplified expression with only positive exponents.