Question

simplify the expression.
(1) $9^2 + 3 \cdot 5$
(2) $4^3 - 30 \div 2$
(3) $9 + 45 \div 9 \cdot 8$
(4) $7^2 - 14 + 5 \cdot 2$
(5) $2^3 + 6(3 + 10)$
(6) $8^2 - (8 - 4)$
(7) $14 + (3^3 - 7)$
(8) $20 \div (4 - (10 - 8))$
(9) $\frac{18 + 10}{7 - 3}$
(10) $8 - 3(2 - (3 + 1)^2 \div 8 \cdot 2)$
(11) $3^2 + 5(2 + 9)$
(12) $7^2 - 8 \cdot 3 + 6$
(13) $3 \cdot 5 - (3^2 + 2) + 72 \div 8$
(14) $8 - 3 - (24 - 4^2) \div 2$
(15) $11 + 3(19 + 2)$
(16) $6(5 + 3) - 4(6 - 3)$
(17) $10 + 2 \cdot 18 \div (5 + 1)$
(18) $(6 \div 2) \cdot 9 \div 18$

Explanation:

Let's solve these expressions one by one using the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

(1) \( 9^2 + 3 \cdot 5 \)

Step1: Calculate the exponent and multiplication

\( 9^2 = 81 \), \( 3 \cdot 5 = 15 \)

Step2: Add the results

\( 81 + 15 = 96 \)

Answer:

\( 96 \)

(2) \( 4^3 - 30 \div 2 \)

Step1: Calculate the exponent and division

\( 4^3 = 64 \), \( 30 \div 2 = 15 \)

Step2: Subtract the results

\( 64 - 15 = 49 \)