Simplify each expression using the correct order of operations:

$(-3)^2 - 2 \times (-9) + 6$
$3 \times 10 + 4 - 4^2$
$(-9) - (-8) + 2 \times 4^2$
$(-3)^3 - 2 + 8 + (-8)$
$8 + (-4) \times (-6)^2 + 7$
$4 \times (-8) + 6 - (-2)^3$
$10 \times 3 - (-6)^2 + (-8)$
$(-5)^2 \times 3 \div 5 + 9$
$(10 \div (-5) - (-2)) \times (-3)^3$
$4 \times (-6) \div 8 + 3^3$

Question

04-11-2026
Mathematics

Answered

Simplify each expression using the correct order of operations:

$(-3)^2 - 2 \times (-9) + 6$
$3 \times 10 + 4 - 4^2$
$(-9) - (-8) + 2 \times 4^2$
$(-3)^3 - 2 + 8 + (-8)$
$8 + (-4) \times (-6)^2 + 7$
$4 \times (-8) + 6 - (-2)^3$
$10 \times 3 - (-6)^2 + (-8)$
$(-5)^2 \times 3 \div 5 + 9$
$(10 \div (-5) - (-2)) \times (-3)^3$
$4 \times (-6) \div 8 + 3^3$

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-04T15:49:08-05:00

Use the order of operations (PEMDAS) to process each expression consistently: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Evaluate exponents and parentheses first, followed by sequential multiplication, division, addition, and subtraction.
Compute the values for all 10 expressions carefully, ensuring sign changes and grouping symbols are handled correctly.
The results are: $1. 33, 2. 18, 3. 31, 4. -29, 5. -129, 6. -18, 7. -14, 8. 24, 9. 0, 10. 24$, so $\boxed{33, 18, 31, -29, -129, -18, -14, 24, 0, 24}$.

Explanation

Understanding the Order of Operations

To simplify these arithmetic expressions, we follow the order of operations, often referred to as PEMDAS:

Parentheses: Solve operations inside grouping symbols first.
Exponents: Calculate powers.
Multiplication and Division: Perform these from left to right.
Addition and Subtraction: Perform these from left to right.

By systematically applying these rules to each expression, we can obtain the correct values.

Simplifying Expressions 1-5
$(-3)^2 - 2 \times (-9) + 6$: First, calculate the exponent $(-3)^2 = 9$. Then, multiply $-2 \times (-9) = 18$. Finally, add: $9 + 18 + 6 = 33$.
$3 \times 10 + 4 - 4^2$: First, calculate the exponent $4^2 = 16$. Multiply $3 \times 10 = 30$. Then, perform addition and subtraction: $30 + 4 - 16 = 34 - 16 = 18$.
$(-9) - (-8) + 2 \times 4^2$: First, calculate the exponent $4^2 = 16$. Multiply $2 \times 16 = 32$. Then, evaluate: $-9 + 8 + 32 = -1 + 32 = 31$.
$(-3)^3 - 2 + 8 + (-8)$: Calculate the exponent $(-3)^3 = -27$. Then, evaluate: $-27 - 2 + 8 - 8 = -29$.
$8 + (-4) \times (-6)^2 + 7$: Calculate the exponent $(-6)^2 = 36$. Multiply $-4 \times 36 = -144$. Then, evaluate: $8 - 144 + 7 = 15 - 144 = -129$.

Simplifying Expressions 6-10
$4 \times (-8) + 6 - (-2)^3$: Calculate the exponent $(-2)^3 = -8$. Multiply $4 \times (-8) = -32$. Then, evaluate: $-32 + 6 - (-8) = -32 + 6 + 8 = -18$.
$10 \times 3 - (-6)^2 + (-8)$: Calculate the exponent $(-6)^2 = 36$. Multiply $10 \times 3 = 30$. Then, evaluate: $30 - 36 - 8 = -6 - 8 = -14$.
$(-5)^2 \times 3 \div 5 + 9$: Calculate the exponent $(-5)^2 = 25$. Multiply and divide from left to right: $25 \times 3 = 75$, $75 \div 5 = 15$. Finally, add: $15 + 9 = 24$.
$(10 \div (-5) - (-2)) \times (-3)^3$: Solve inside the parentheses: $10 \div (-5) = -2$, then $-2 - (-2) = -2 + 2 = 0$. Calculate the exponent $(-3)^3 = -27$. Multiply: $0 \times (-27) = 0$.
$4 \times (-6) \div 8 + 3^3$: Calculate the exponent $3^3 = 27$. Multiply and divide: $4 \times (-6) = -24$, then $-24 \div 8 = -3$. Finally, add: $-3 + 27 = 24$.

Conclusion

The results of the calculations are:

33
18
31
-29
-129
-18
-14
24
0
24

Thus, the final results are $\boxed{33, 18, 31, -29, -129, -18, -14, 24, 0, 24}$.

Examples

Knowing the correct order of operations is essential for everyday financial calculations or programming. For example, if you are calculating the total cost of a project involving a fixed overhead fee, multiple material quantities, and discounted rates, you must apply operations in the correct order to ensure the result is accurate. Mistakes in order can lead to incorrect budgeting, faulty construction estimates, or software bugs. Understanding these rules acts as a fundamental tool for precision and problem-solving in any technical or financial field.