1. **State the problem:** Simplify and evaluate the expression $$44^{\frac{7}{8}} \cdot 44^{\frac{3}{4}}$$. 2. **Use the property of exponents:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Add the exponents:** $$\frac{7}{8} + \frac{3}{4} = \frac{7}{8} + \frac{3 \times 2}{4 \times 2} = \frac{7}{8} + \frac{6}{8} = \frac{7+6}{8} = \frac{13}{8}$$ 4. **Rewrite the expression:** $$44^{\frac{7}{8}} \cdot 44^{\frac{3}{4}} = 44^{\frac{13}{8}}$$ 5. **Evaluate the expression:** Calculate $$44^{\frac{13}{8}} = \left(44^{\frac{1}{8}}\right)^{13}$$. Using a calculator: $$44^{\frac{1}{8}} \approx 1.62657$$ Then: $$1.62657^{13} \approx 357.55$$ 6. **Final answer:** $$44^{\frac{7}{8}} \cdot 44^{\frac{3}{4}} = 44^{\frac{13}{8}} \approx 357.55$$