1. **State the problem:** Evaluate the expression $$3 \times 9^0 \div 2 \times (2^2 + 3^0 + 13) - 3 \times \left(2^5 \div 8\right)$$. 2. **Recall important rules:** - Any number raised to the power 0 is 1, i.e., $9^0 = 1$ and $3^0 = 1$. - Follow the order of operations: parentheses, exponents, multiplication and division (left to right), addition and subtraction. 3. **Evaluate powers:** $$9^0 = 1$$ $$3^0 = 1$$ $$2^2 = 4$$ $$2^5 = 32$$ 4. **Substitute values into the expression:** $$3 \times 1 \div 2 \times (4 + 1 + 13) - 3 \times \left(32 \div 8\right)$$ 5. **Simplify inside the parentheses:** $$4 + 1 + 13 = 18$$ 6. **Rewrite expression:** $$3 \times 1 \div 2 \times 18 - 3 \times 4$$ 7. **Perform multiplication and division from left to right:** First, $$3 \times 1 = 3$$ Then, $$3 \div 2 = \frac{3}{2}$$ Show cancellation: $$\frac{\cancel{3}}{\cancel{2}}$$ (no common factors to cancel here, so it remains $\frac{3}{2}$) Next, multiply by 18: $$\frac{3}{2} \times 18 = \frac{3 \times 18}{2} = \frac{54}{2}$$ Simplify fraction: $$\frac{54}{2} = 27$$ 8. **Calculate the second term:** $$3 \times 4 = 12$$ 9. **Final calculation:** $$27 - 12 = 15$$ **Final answer:** $15$