1. **Stating the problem:** Simplify and solve the expression $+(15) \times [(35)^2 = (-3)^{31}] = [(23)^2 = (2^a)]$. 2. **Clarify the expression:** The expression seems to have some syntax issues. Assuming the problem is to evaluate and compare powers and solve for $a$ in the equation: $$ (35)^2 = (-3)^{31} = (23)^2 = (2^a) $$ 3. **Calculate each term:** - Calculate $(35)^2$: $$ 35^2 = 1225 $$ - Calculate $(-3)^{31}$: Since 31 is odd, $(-3)^{31} = -3^{31}$, which is a very large negative number. - Calculate $(23)^2$: $$ 23^2 = 529 $$ 4. **Analyze equality:** - $1225 \neq -3^{31}$ (positive vs large negative), so equality does not hold. - $1225 \neq 529$, so equality does not hold. 5. **Assuming the problem is to solve for $a$ in $529 = 2^a$:** $$ 2^a = 529 $$ 6. **Solve for $a$ using logarithms:** $$ a = \log_2 529 $$ 7. **Calculate $a$ approximately:** Using change of base formula: $$ a = \frac{\log_{10} 529}{\log_{10} 2} \approx \frac{2.723}{0.301} \approx 9.05 $$ **Final answer:** $$ a \approx 9.05 $$