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Order of Operations with Exponents

Students will be able to correctly evaluate numerical expressions using the order of operations, including exponents.

Original question

Why this classification?

The question requires students to evaluate a numerical expression involving exponents, parentheses, multiplication, division, addition, and subtraction. The key skill is applying the order of operations (PEMDAS/BODMAS), including exponents, to simplify the expression. Among the TEKS candidates, math:6.7A is the only standard that explicitly requires generating equivalent numerical expressions using order of operations, including whole-number exponents. Other candidates either do not include exponents (math:5.4F) or focus on different operations or problem types. Therefore, math:6.7A is the best match. The grade level confidence is high because the standard directly matches the skill and grade context. The question is multiple-choice and on grade level for this standard.

TEKS: Apply order of operations with whole-number exponents.

Concepts: order of operations, exponents, numerical expressions, parentheses, multiplication and division

Grounded classification

Retrieved 10 database candidates. The model selected a verified record. Official web evidence was also consulted.

Sources: Selected TEKS record, Grade 6 Middle School Advanced Mathematics TEKS Crosswalk Rev 5-15-2025, Middle School Advanced Mathematics | Texas Education Agency, 2023 STAAR Grade 6 Math Rationales

How it works

When you see a math expression with different operations—like parentheses, exponents, multiplication, division, addition, and subtraction—you need to solve it in a special order. This is called the order of operations. You can remember it with the phrase PEMDAS:

Parentheses first
Exponents next
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Let's look at an expression with all these parts: 3 + 2^3 × (10 - 4) ÷ 4.

Parentheses: Solve anything inside ( ).
Exponents: Solve numbers with exponents (like 2^3).
Multiplication and Division: Go left to right across the expression.
Addition and Subtraction: Go left to right across the expression.

Always work step-by-step, writing down each part as you go.

Before you start: Know what exponents are (e.g., 2^3 means 2 × 2 × 2). · Understand basic operations: addition, subtraction, multiplication, division. · Be familiar with parentheses in math expressions.

Worked example

Evaluate: 5 + 3^2 × (8 - 2) ÷ 2

Follow the reasoning

1
Step 1: Parentheses
Work out the part in ( ). 8 - 2 = 6, so rewrite as 5 + 3^2 × 6 ÷ 2
2
Step 2: Exponents
Calculate 3^2. That's 3 × 3 = 9. Now the expression is 5 + 9 × 6 ÷ 2
3
Step 3: Multiplication and Division (left to right)
Start with 9 × 6 = 54. Now it's 5 + 54 ÷ 2. Next, 54 ÷ 2 = 27. Now it's 5 + 27
4
Step 4: Addition
Finally, add: 5 + 27 = 32.

Answer

Common mistakes

01
Doing addition before multiplication or division
Why: Some students just go left to right without following PEMDAS.
Avoid it: Always do multiplication and division before addition and subtraction.
02
Ignoring exponents or solving them last
Why: Students might skip exponents or not notice them.
Avoid it: After parentheses, always look for exponents next.
03
Doing division before multiplication, or vice versa, not left to right
Why: Students might think multiplication always comes before division.
Avoid it: Do multiplication and division as you see them, moving left to right.

Practice

Answers stay hidden

1.4 + 2^2 × (6 - 1) ÷ 5
Show hint
Follow PEMDAS. Start with the parentheses, then exponents.
Reveal answer
6
2.7 + 3^2 × (5 + 1) ÷ 2
Show hint
Work inside the parentheses first.
Reveal answer
34
3.2 + 5^2 × (9 - 4) ÷ 5
Show hint
Calculate the exponent before multiplying.
Reveal answer
27

Submitted Oct 12, 2026, 4:10 AM · gpt-4.1-2025-04-14 in 10020 ms · gpt-4.1-2025-04-14 in 5797 ms

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