1. **State the problem:** Simplify each expression using exponential notation. 2. **Expression 1:** $$\frac{4^2 y^8}{4^3 y^2}$$ - Use the rule $$\frac{a^m}{a^n} = a^{m-n}$$ for both bases 4 and y. - Simplify numerator and denominator separately: $$4^{2-3} y^{8-2} = 4^{-1} y^6$$ - Rewrite negative exponent: $$\frac{y^6}{4}$$ 3. **Expression 2:** $$\frac{y^6}{4}$$ - This is already simplified. 4. **Expression 3:** $$4 y^6$$ - This is already simplified. 5. **Expression 4:** $$y^6 \times 4$$ - Multiplication is commutative, so this equals $$4 y^6$$, already simplified. 6. **Expression 5:** $$\frac{4}{y^6}$$ - This is already simplified. **Final simplified expressions:** - $$\frac{y^6}{4}$$ - $$\frac{y^6}{4}$$ - $$4 y^6$$ - $$4 y^6$$ - $$\frac{4}{y^6}$$