1. **Problem 1:** Simplify the expression $\frac{a^2 - b^2}{a + b}$. 2. **Formula and rules:** Recall the difference of squares factorization: $$a^2 - b^2 = (a - b)(a + b)$$ 3. **Step-by-step simplification:** $$\frac{a^2 - b^2}{a + b} = \frac{(a - b)(a + b)}{a + b}$$ 4. Cancel the common factor $a + b$ (assuming $a + b \neq 0$): $$\frac{\cancel{(a + b)}(a - b)}{\cancel{a + b}} = a - b$$ 5. **Final answer for Problem 1:** $$a - b$$ 6. **Problem 2:** For a non-zero rational number $z$, find the value of $(z^{23})^{\frac{1}{5}}$. 7. **Formula and rules:** Use the power of a power rule: $$\left(z^m\right)^n = z^{m \times n}$$ 8. Apply the rule: $$\left(z^{23}\right)^{\frac{1}{5}} = z^{23 \times \frac{1}{5}} = z^{\frac{23}{5}}$$ 9. None of the options exactly match $z^{\frac{23}{5}}$, so check if the question might mean $(z^{2})^{3}$ or similar. Since options are $z^6$, $z^{-5}$, $z^1$, $z^4$, none equal $z^{\frac{23}{5}}$. 10. If the question is about $(z^{2})^{3}$, then: $$\left(z^2\right)^3 = z^{2 \times 3} = z^6$$ 11. **Final answer for Problem 2:** If the expression is $(z^{23})^{1/5}$, answer is $z^{\frac{23}{5}}$ (not listed). If the expression is $(z^2)^3$, answer is $z^6$ (option a). **Summary:** - Problem 1 answer: $a - b$ - Problem 2 answer: $z^{\frac{23}{5}}$ (or $z^6$ if question intended $(z^2)^3$)