This question tests evaluating numerical expressions with whole-number exponents like 2³ using the order of operations, often remembered as PEMDAS, where exponents are evaluated before multiplication 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 3 × 2², step 1: compute 2² = 4, step 2: multiply 3 × 4 = 12; 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 6 + 2³ × 3, first evaluate the exponent: 2³ = 8, then multiply 8 × 3 = 24, and finally add 6 + 24 = 30. A common error is adding before multiplying, like 6 + 2³ = 8 then 8 × 3 = 24, or treating exponent as multiplication such as 2³ = 6 then 6 + 6 × 3 = 6 + 18 = 24, or violating order by doing 2³ × 3 = 24 but then adding wrongly. To solve these, use this strategy: (1) scan for parentheses and compute inside them first, (2) identify and evaluate all exponents like 2³, (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 8 × 3 = 24 plus 6 is 30. 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 2⁴ and 3² using the order of operations, often remembered as PEMDAS, where exponents are evaluated before 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 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 2⁴ + 3², evaluate the exponents: 2⁴ = 16 and 3² = 9, then add 16 + 9 = 25. A common error is treating exponent as multiplication like 2⁴ = 2 × 4 = 8, then 8 + 9 = 17, or adding before exponents which isn't possible here, or arithmetic error like 16 + 9 = 24. To solve these, use this strategy: (1) scan for parentheses and compute inside them first, (2) identify and evaluate all exponents like 2⁴ or 3², (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 16 + 9 = 25. 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, ignoring parentheses, or adding before exponentiating.

This question tests evaluating numerical expressions with whole-number exponents like $ (2 + 6)^2 $ using the order of operations, often remembered as PEMDAS, where parentheses are handled first before exponents. Exponent notation means the base is multiplied by itself as many times as the exponent indicates, so $ 2^3 = 2 \times 2 \times 2 = 8 $, not $ 2 \times 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 $ 5^2 = 25 $, (3) multiply or divide from left to right, and (4) add or subtract from left to right; for instance, in $ 3 \times 2^2 + 4 $, you do the exponent $ 2^2 = 4 $ first, then multiply $ 3 \times 4 = 12 $, then add $ 12 + 4 = 16 $; when there are multiple exponents, evaluate each one independently, such as in $ 2^3 + 4^2 $ where $ 2^3 = 8 $ and $ 4^2 = 16 $, then add to get 24. For example, to evaluate $ (2 + 3)^2 $, step 1: compute inside parentheses 2 + 3 = 5, step 2: then exponent $ 5^2 = 25 $; or for $ 2^3 + 4^2 $, step 1: $ 2^3 = 8 $, step 2: $ 4^2 = 16 $, step 3: $ 8 + 16 = 24 $; or for $ 3 \times 2^2 $, step 1: $ 2^2 = 4 $, step 2: $ 3 \times 4 = 12 $. For the expression $ (2 + 6)^2 $, first evaluate inside the parentheses: 2 + 6 = 8, then apply the exponent: $ 8^2 = 64 $. A common error is ignoring parentheses and computing $ 2^2 + 6^2 = 4 + 36 = 40 $, or distributing the exponent wrongly like $ (2)^2 + (6)^2 $ instead of adding first, or arithmetic error like $ 8^2 = 68 $. To solve these, use this strategy: (1) scan for parentheses and compute inside them first, (2) identify and evaluate all exponents like the resulting base squared, (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 $ 8^2 $ should be 64. Remember common exponents: $ 2^2 = 4 $, $ 2^3 = 8 $, $ 2^4 = 16 $, $ 3^2 = 9 $, $ 3^3 = 27 $, $ 4^2 = 16 $, $ 5^2 = 25 $, $ 10^2 = 100 $, $ 10^3 = 1000 $; avoid mistakes like treating exponents as multiplication, violating order, ignoring parentheses by squaring each term separately, or adding before exponentiating when parentheses require otherwise.

This question tests evaluating numerical expressions with whole-number exponents like 4², 2⁴, and 2² 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 4² + 2⁴ ÷ 2², compute exponents: 4² = 16, 2⁴ = 16, 2² = 4, then divide 16 ÷ 4 = 4, finally add 16 + 4 = 20. A common error is adding before dividing, like 2⁴ + 2² = 16 + 4 = 20, then 4² + 20 = 16 + 20 = 36, or treating division as lower priority incorrectly. The strategy is to (1) scan for parentheses (none), (2) evaluate all exponents (4² = 16, 2⁴ = 16, 2² = 4), (3) divide left to right (16 ÷ 4 = 4), (4) add (16 + 4 = 20), and (5) verify reasonableness, like 16 + 4 = 20. Common exponents: 2⁴ = 16, 4² = 16; mistakes include confusing 2⁴ ÷ 2² as (2 ÷ $2)^{4-2}$ = 1² = 1 instead of 16 ÷ 4 = 4.

This question tests evaluating numerical expressions with whole-number exponents like 10² and 6² 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 10² - 6², compute the exponents first: 10² = 100 and 6² = 36, then subtract 100 - 36 = 64. A common error is treating exponents as multiplication, like 10² = 20, leading to 20 - 12 = 8, or subtracting before exponentiating like 10 - 6 = 4, then 4² = 16. The strategy is to (1) scan for parentheses (none here), (2) evaluate all exponents first (10² = 100, 6² = 36), (3) no multiplication or division, (4) subtract left to right (100 - 36 = 64), and (5) verify if reasonable, like 100 - 36 is about 60-70. Common exponents to memorize include 10² = 100, 6² = 36; mistakes often involve arithmetic errors like 100 - 36 = 74 or confusing with difference of squares formula unnecessarily here.

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 4², 2⁴, and 2² 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 4² + 2⁴ ÷ 2², compute exponents: 4² = 16, 2⁴ = 16, 2² = 4, then divide 16 ÷ 4 = 4, finally add 16 + 4 = 20. A common error is adding before dividing, like 2⁴ + 2² = 16 + 4 = 20, then 4² + 20 = 16 + 20 = 36, or treating division as lower priority incorrectly. The strategy is to (1) scan for parentheses (none), (2) evaluate all exponents (4² = 16, 2⁴ = 16, 2² = 4), (3) divide left to right (16 ÷ 4 = 4), (4) add (16 + 4 = 20), and (5) verify reasonableness, like 16 + 4 = 20. Common exponents: 2⁴ = 16, 4² = 16; mistakes include confusing 2⁴ ÷ 2² as (2 ÷ $2)^{4-2}$ = 1² = 1 instead of 16 ÷ 4 = 4.

This question tests evaluating numerical expressions with whole-number exponents like $10^2$ and $6^2$ 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 $10^2 - 6^2$, compute the exponents first: $10^2 = 100$ and $6^2 = 36$, then subtract $100 - 36 = 64$. A common error is treating exponents as multiplication, like $10^2 = 20$, leading to $20 - 12 = 8$, or subtracting before exponentiating like $10 - 6 = 4$, then $4^2 = 16$. The strategy is to (1) scan for parentheses (none here), (2) evaluate all exponents first ($10^2 = 100$, $6^2 = 36$), (3) no multiplication or division, (4) subtract left to right ($100 - 36 = 64$), and (5) verify if reasonable, like $100 - 36$ is about 60-70. Common exponents to memorize include $10^2 = 100$, $6^2 = 36$; mistakes often involve arithmetic errors like $100 - 36 = 74$ or confusing with difference of squares formula unnecessarily here.

This question tests evaluating numerical expressions with whole-number exponents like 5² and 3² 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 3² = 3 × 3 = 9, not 3 × 2 = 6; follow PEMDAS by handling parentheses first, then exponents, multiplication/division left to right, and addition/subtraction left to right, for example, in 4² - 2 × 3, compute 4² = 16 first, then 2 × 3 = 6, then 16 - 6 = 10. For example, to evaluate 3² - 2², step 1: 3² = 9, step 2: 2² = 4, step 3: 9 - 4 = 5; or for 2 × 3², step 1: 3² = 9, step 2: 2 × 9 = 18; or for (2 + 3)², step 1: 2 + 3 = 5, step 2: 5² = 25. For 5² - 2 × 3², first compute exponents: 5² = 25 and 3² = 9, then multiply 2 × 9 = 18, and subtract 25 - 18 = 7. A common error is violating order by subtracting first like 5² - 2 = 23 then × 3² = 23 × 9 = 207, or treating exponents as multiplication like 3² = 6 leading to 25 - 2 × 6 = 25 - 12 = 13, or multiplying wrongly. The strategy is to (1) scan for parentheses and compute inside first, (2) evaluate all exponents like 5² and 3², (3) multiply/divide left to right, (4) add/subtract left to right, and (5) verify reasonable, such as 25 - 18 equaling 7. Common exponents to know include 2² = 4, 3² = 9, 5² = 25; mistakes often involve subtracting before multiplying.