This question tests evaluating numerical expressions with whole-number exponents like $2^2$ using the order of operations (PEMDAS: parentheses first, then exponents, multiplication and division left to right, addition and subtraction left to right). Exponent notation means the base is multiplied by itself the number of times indicated by the exponent, so $2^3 = 2 \times 2 \times 2 = 8$, not $2 \times 3 = 6$; follow PEMDAS strictly, for example, in $3 \times 2^2 + 4$, compute $2^2 = 4$ first, then $3 \times 4 = 12$, then $12 + 4 = 16$; with multiple exponents, evaluate each one separately before other operations. For example, to evaluate $2^3 + 4^2$, step 1: $2^3 = 2 \times 2 \times 2 = 8$, step 2: $4^2 = 4 \times 4 = 16$, step 3: $8 + 16 = 24$; or for $3 \times 2^2$, step 1: $2^2 = 4$, step 2: $3 \times 4 = 12$; or for $(2 + 3)^2$, step 1: $2 + 3 = 5$, step 2: $5^2 = 25$. For $6 \times 2^2 - 10$, compute exponent $2^2 = 4$, then multiply $6 \times 4 = 24$, finally subtract $24 - 10 = 14$. A common error is multiplying before exponent, like $(6 \times 2)^2 - 10 = 12^2 - 10 = 144 - 10 = 134$, or treating exponent as multiplication $6 \times 2 \times 2 - 10 = 24 - 10 = 14$ (coincidentally correct but wrong reason). The strategy is to (1) scan for parentheses (none), (2) evaluate exponents ($2^2 = 4$), (3) multiply ($6 \times 4 = 24$), (4) subtract ($24 - 10 = 14$), and (5) check if about 20-10=10ish, but precisely 14. Common exponents: $2^2 = 4$; mistakes include subtracting first $2^2 - 10 = -6$, then $6 \times -6 = -36$, or arithmetic $24 - 10 = 12$.

This question tests evaluating numerical expressions with whole-number exponents like $10^2$ and $5^2$ using order of operations (PEMDAS: exponents before multiplication/addition, parentheses first). Exponent notation means the base is multiplied by itself the number of times indicated by the exponent, so $5^2 = 5 \times 5 = 25$, not $5 \times 2 = 10$; follow PEMDAS by handling parentheses first, then exponents, multiplication/division left to right, and addition/subtraction left to right, for example, in $4^2 \div 2^2$, compute exponents to $16 \div 4 = 4$. For example, to evaluate $2^3 \div 2^2$, step 1: $2^3 = 8$, step 2: $2^2 = 4$, step 3: $8 \div 4 = 2$; or for $3 \times 2^2$, step 1: $2^2 = 4$, step 2: $3 \times 4 = 12$; or for $(2 + 3)^2$, step 1: $2 + 3 = 5$, step 2: $5^2 = 25$. For $10^2 \div 5^2$, first compute exponents: $10^2 = 100$ and $5^2 = 25$, then divide $100 \div 25 = 4$. A common error is treating exponents as multiplication, like $10^2 = 20$ leading to $20 \div 10 = 2$, or violating order by dividing bases first as $(10 \div 5)^2 = 2^2 = 4$ (which coincidentally matches but is wrong process), or arithmetic errors like $100 \div 25 = 5$. The strategy is to (1) scan for parentheses and compute inside first, (2) evaluate all exponents like $10^2$ and $5^2$, (3) multiply/divide left to right, (4) add/subtract if present left to right, and (5) verify the result is reasonable, such as $100 \div 25$ equaling 4. Common exponents to know include $2^2 = 4$, $5^2 = 25$, $10^2 = 100$; mistakes often involve confusing division of powers with other operations.

This question tests evaluating numerical expressions with whole-number exponents like ² and 2³ using the order of operations (PEMDAS: parentheses first, then exponents, multiplication and division left to right, addition and subtraction left to right). Exponent notation means the base is multiplied by itself the number of times indicated by the exponent, so 2³ = 2 × 2 × 2 = 8, not 2 × 3 = 6; follow PEMDAS strictly, for example, in 3 × 2² + 4, compute 2² = 4 first, then 3 × 4 = 12, then 12 + 4 = 16; with multiple exponents, evaluate each one separately before other operations. For example, to evaluate 2³ + 4², step 1: 2³ = 2 × 2 × 2 = 8, step 2: 4² = 4 × 4 = 16, step 3: 8 + 16 = 24; or for 3 × 2², step 1: 2² = 4, step 2: 3 × 4 = 12; or for (2 + 3)², step 1: 2 + 3 = 5, step 2: 5² = 25. For (9 - 4)² + 2³, first parentheses: 9 - 4 = 5, then 5² = 25, next 2³ = 8, finally add 25 + 8 = 33. A common error is ignoring parentheses, like 9² - 4² + 2³ = 81 - 16 + 8 = 73, or distributing exponent wrongly as 9² + (-4)² = 81 + 16 = 97 + 8. The strategy is to (1) compute inside parentheses first (9 - 4 = 5), (2) evaluate exponents (5² = 25, 2³ = 8), (3) no multiply/divide, (4) add (25 + 8 = 33), and (5) verify, like 25 + 8 is about 30-35. Common exponents: 5² = 25, 2³ = 8; mistakes include arithmetic 25 + 8 = 23 or forgetting to square after subtracting.

This question tests evaluating numerical expressions with whole-number exponents like 2² using order of operations (PEMDAS: exponents before multiplication/addition, parentheses first). Exponent notation means the base is multiplied by itself the number of times indicated by the exponent, so 2² = 2 × 2 = 4, not 2 × 2 = 4 wait, but common mistake is thinking it's base times exponent directly; follow PEMDAS by handling parentheses first, then exponents, multiplication/division left to right, and addition/subtraction left to right, for example, in 3 × 2², compute 2² = 4 first, then 3 × 4 = 12. For example, to evaluate 3 × 2², step 1: 2² = 4, step 2: 3 × 4 = 12; or for (3 × 2)², step 1: 3 × 2 = 6 inside implied, but actually parentheses would make it 36; or for 2³, step 1: 2 × 2 × 2 = 8. The student claims 3 × 2² = 36, but correctly it's first 2² = 4, then 3 × 4 = 12. A common error is violating order by multiplying first then exponentiating as (3 × 2)² = 6² = 36, which is what the student did, or treating exponent as addition like 3 × (2 + 2) = 12, or other arithmetic. The strategy is to (1) scan for parentheses, (2) evaluate exponents like 2² first, (3) multiply/divide left to right, (4) add/subtract if present, and (5) verify by knowing 2² = 4, times 3 is 12. Common exponents to know include 2² = 4, 2³ = 8; mistakes like this often come from confusing multiplication and exponentiation order.

This question tests evaluating numerical expressions with whole-number exponents like 4² and 2³ using order of operations (PEMDAS: exponents before multiplication/addition, parentheses first). Exponent notation means the base is multiplied by itself the number of times indicated by the exponent, so 4² = 4 × 4 = 16, not 4 × 2 = 8; follow PEMDAS by handling parentheses first, then exponents, multiplication/division left to right, and addition/subtraction left to right, for example, in 3 × 2² + 4, compute 2² = 4 first, then 3 × 4 = 12, then 12 + 4 = 16, and with multiple exponents like 2³ + 4², evaluate each separately to get 8 + 16 = 24. For example, to evaluate 2³ + 4², step 1: 2³ = 8, step 2: 4² = 16, step 3: 8 + 16 = 24; or for 3 × 2², step 1: 2² = 4, step 2: 3 × 4 = 12; or for (2 + 3)², step 1: 2 + 3 = 5, step 2: 5² = 25. For 4² + 3 × 2³, first compute exponents: 4² = 16 and 2³ = 8, then multiply 3 × 8 = 24, and add 16 + 24 = 40. A common error is violating order by multiplying bases first like (4 + 3 × 2)³ which is incorrect, or treating exponents as multiplication like 2³ = 6 leading to 16 + 3 × 6 = 16 + 18 = 34, or adding before multiplying. The strategy is to (1) scan for parentheses and compute inside first, (2) evaluate all exponents like 4² and 2³, (3) multiply/divide left to right, (4) add/subtract left to right, and (5) verify the result is reasonable, such as 16 + 24 equaling 40. Common exponents to know include 2³ = 8, 3² = 9, 4² = 16; mistakes often involve incorrect order like (4 + 3) × 2³ = 7 × 8 = 56.

This question tests evaluating numerical expressions with whole-number exponents like 3⁴ and 2³ using the order of operations (PEMDAS: parentheses first, then exponents, multiplication and division left to right, addition and subtraction left to right). Exponent notation means the base is multiplied by itself the number of times indicated by the exponent, so 2³ = 2 × 2 × 2 = 8, not 2 × 3 = 6; follow PEMDAS strictly, for example, in 3 × 2² + 4, compute 2² = 4 first, then 3 × 4 = 12, then 12 + 4 = 16; with multiple exponents, evaluate each one separately before other operations. For example, to evaluate 2³ + 4², step 1: 2³ = 2 × 2 × 2 = 8, step 2: 4² = 4 × 4 = 16, step 3: 8 + 16 = 24; or for 3 × 2², step 1: 2² = 4, step 2: 3 × 4 = 12; or for (2 + 3)², step 1: 2 + 3 = 5, step 2: 5² = 25. For 3⁴ - 2³, compute exponents: 3⁴ = 81 (3×3×3×3), 2³ = 8, then subtract 81 - 8 = 73. A common error is treating as (3 - $2)^4$ ^3 or something, or computing $3^4$ as 3×4=12, leading to 12 - 8 = 4. The strategy is to (1) scan for parentheses (none), (2) evaluate exponents (3⁴ = 81, 2³ = 8), (3) no multiply/divide, (4) subtract (81 - 8 = 73), and (5) verify, like 81 - 8 about 70-80. Common exponents: 3⁴ = 81, 2³ = 8; mistakes include 3⁴ as $3^2$=9 ×2=18 or arithmetic 81 - 8 = 72.

This question tests evaluating numerical expressions with whole-number exponents like 8² and 4² using the order of operations, often remembered as PEMDAS, where exponents are evaluated before division and addition, and parentheses come first. Exponent notation means the base is multiplied by itself as many times as the exponent indicates, so 2³ = 2 × 2 × 2 = 8, not 2 × 3 = 6; the order of operations is: (1) parentheses first, for example in (2 + 3)² you compute 2 + 3 = 5 first, (2) then exponents like 5² = 25, (3) multiply or divide from left to right, and (4) add or subtract from left to right; for instance, in 3 × 2² + 4, you do the exponent 2² = 4 first, then multiply 3 × 4 = 12, then add 12 + 4 = 16; when there are multiple exponents, evaluate each one independently, such as in 2³ + 4² where 2³ = 8 and 4² = 16, then add to get 24. For example, to evaluate 10² ÷ 5², step 1: 10² = 100, step 2: 5² = 25, step 3: 100 ÷ 25 = 4; or for 2³ + 4², step 1: 2³ = 8, step 2: 4² = 16, step 3: 8 + 16 = 24; or for (2 + 3)², step 1: 2 + 3 = 5, step 2: 5² = 25. For the expression 8² ÷ 4² + 3, first evaluate the exponents: 8² = 64 and 4² = 16, then divide 64 ÷ 16 = 4, and finally add 4 + 3 = 7. A common error is adding before dividing like 4² + 3 = 16 + 3 = 19 then 8² ÷ 19 which is wrong, or violating order by doing division after addition, or treating exponent as multiplication such as 4² = 4 × 2 = 8 then 64 ÷ 8 + 3 = 8 + 3 = 11. To solve these, use this strategy: (1) scan for parentheses and compute inside them first, (2) identify and evaluate all exponents like 8² or 4², (3) multiply or divide from left to right if present, (4) add or subtract from left to right, and (5) verify if the result is reasonable, such as 64 ÷ 16 = 4 plus 3 is 7. Remember common exponents: 2² = 4, 2³ = 8, 2⁴ = 16, 3² = 9, 3³ = 27, 4² = 16, 5² = 25, 10² = 100, 10³ = 1000; avoid mistakes like treating exponents as multiplication, violating order by adding first, ignoring parentheses, or adding before exponentiating.

This question tests evaluating numerical expressions with whole-number exponents like 5² and 2² using the order of operations, often remembered as PEMDAS, where exponents are evaluated before multiplication and subtraction, and parentheses come first. Exponent notation means the base is multiplied by itself as many times as the exponent indicates, so 2³ = 2 × 2 × 2 = 8, not 2 × 3 = 6; the order of operations is: (1) parentheses first, for example in (2 + 3)² you compute 2 + 3 = 5 first, (2) then exponents like 5² = 25, (3) multiply or divide from left to right, and (4) add or subtract from left to right; for instance, in 3 × 2² + 4, you do the exponent 2² = 4 first, then multiply 3 × 4 = 12, then add 12 + 4 = 16; when there are multiple exponents, evaluate each one independently, such as in 2³ + 4² where 2³ = 8 and 4² = 16, then add to get 24. For example, to evaluate 2³ + 4², step 1: compute 2³ = 2 × 2 × 2 = 8, step 2: compute 4² = 4 × 4 = 16, step 3: add 8 + 16 = 24; or for 3 × 2², step 1: 2² = 4, step 2: 3 × 4 = 12; or for (2 + 3)², step 1: 2 + 3 = 5, step 2: 5² = 25. For the expression 5² - 3 × 2², first evaluate the exponents: 5² = 25 and 2² = 4, then multiply 3 × 4 = 12, and finally subtract 25 - 12 = 13. A common error is violating order by multiplying before exponents, like doing 3 × 2 = 6 then 5² - 6² = 25 - 36 = -11, or treating exponent as multiplication such as 2² = 2 × 2 = 4 correctly but then subtracting before multiplying, or arithmetic error like 25 - 12 = 15. To solve these, use this strategy: (1) scan for parentheses and compute inside them first, (2) identify and evaluate all exponents like 5² or 2², (3) multiply or divide from left to right if present, (4) add or subtract from left to right, and (5) verify if the result is reasonable, such as 5² = 25, minus about 12, around 13. Remember common exponents: 2² = 4, 2³ = 8, 2⁴ = 16, 3² = 9, 3³ = 27, 4² = 16, 5² = 25, 10² = 100, 10³ = 1000; avoid mistakes like treating exponents as multiplication, violating order by multiplying first, ignoring parentheses, or subtracting before exponentiating.

This question tests evaluating numerical expressions with whole-number exponents like ² and 3³ using the order of operations (PEMDAS: parentheses first, then exponents, multiplication and division left to right, addition and subtraction left to right). Exponent notation means the base is multiplied by itself the number of times indicated by the exponent, so 2³ = 2 × 2 × 2 = 8, not 2 × 3 = 6; follow PEMDAS strictly, for example, in 3 × 2² + 4, compute 2² = 4 first, then 3 × 4 = 12, then 12 + 4 = 16; with multiple exponents, evaluate each one separately before other operations. For example, to evaluate 2³ + 4², step 1: 2³ = 2 × 2 × 2 = 8, step 2: 4² = 4 × 4 = 16, step 3: 8 + 16 = 24; or for 3 × 2², step 1: 2² = 4, step 2: 3 × 4 = 12; or for (2 + 3)², step 1: 2 + 3 = 5, step 2: 5² = 25. For (2 + 5)² - 3³, first handle parentheses: 2 + 5 = 7, then exponent 7² = 49, next 3³ = 27, then subtract 49 - 27 = 22. A common error is ignoring parentheses, like 2² + 5² - 3³ = 4 + 25 - 27 = 2, or treating exponent outside as distributing, like 2² + 5² = 29, then -27 = 2. The strategy is to (1) scan for parentheses and compute inside first (2 + 5 = 7), (2) evaluate exponents (7² = 49, 3³ = 27), (3) no multiplication or division, (4) subtract (49 - 27 = 22), and (5) verify reasonableness, like 49 - 27 is about 20-25. Common exponents include 3³ = 27, 7² = 49; mistakes involve arithmetic like 49 - 27 = 32 or forgetting to cube 3 as 9.

This question tests evaluating numerical expressions with whole-number exponents like 5² and 2³ using order of operations (PEMDAS: exponents before multiplication/addition, parentheses first). Exponent notation means the base is multiplied by itself the number of times indicated by the exponent, so 2³ = 2 × 2 × 2 = 8, not 2 × 3 = 6; follow PEMDAS by handling parentheses first, then exponents, multiplication/division left to right, and addition/subtraction left to right, for example, in (3 + 2)², compute inside to 5, then 5² = 25. For example, to evaluate (2 + 3)², step 1: 2 + 3 = 5, step 2: 5² = 25; or for 2³ + 3², step 1: 2³ = 8, step 2: 3² = 9, step 3: 8 + 9 = 17; or for 3 × 2², step 1: 2² = 4, step 2: 3 × 4 = 12. For (8 - 3)² + 2³, first compute inside parentheses: 8 - 3 = 5, then 5² = 25, next 2³ = 8, and add 25 + 8 = 33. A common error is ignoring parentheses like 8 - 3² + 2³ = 8 - 9 + 8 = 7, or distributing exponent wrongly as 8² - 3² + 2³ = 64 - 9 + 8 = 63, or arithmetic like 25 + 8 = 32. The strategy is to (1) scan for parentheses and compute inside first, (2) evaluate all exponents like 5² and 2³, (3) multiply/divide if present, (4) add/subtract left to right, and (5) verify reasonable, such as 25 + 8 equaling 33. Common exponents to know include 2³ = 8, 3² = 9, 5² = 25; mistakes often involve computing exponents before parentheses.