Solve the Expression: 81÷3² + 4² Using Order of Operations

Q: Why can't I just work from left to right like in reading?

Mathematics has a specific order that everyone must follow! Without PEMDAS, the same expression could have multiple answers, which would be chaos. Exponents always come before division and addition.

Q: What does the colon symbol (:) mean in this problem?

The colon (:) means division, just like the ÷ symbol. So $ 81:3^2 $ is the same as $ 81 \div 3^2 $.

Q: How do I remember the order of operations?

Use the acronym PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Many students remember it as "Please Excuse My Dear Aunt Sally."

Q: What if I calculated 81÷3 = 27 first by mistake?

If you get $ 27^2 + 16 = 729 + 16 = 745 $, that's way too big! Always double-check by following PEMDAS: exponents first gives us $ 81 \div 9 + 16 = 25 $.

Q: Is there a way to check my final answer?

Yes! Work backwards or use a calculator following PEMDAS. You can also estimate: $ 81 \div 9 $ is about 9, and $ 4^2 = 16 $, so $ 9 + 16 = 25 $ makes sense!

Order of Operations with Exponents

$81:3^2+4^2=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$81:3^2+4^2=$

Step-by-step solution

First, calculate the powers:

$3^2 = 9$

$4^2 = 16$

Now substitute these values into the expression:

$81:3^2+4^2 = 81:9+16$

Perform the division:

$81 \div 9 = 9$

Finally, add the result to 16:

$9 + 16 = 25$

Final Answer

$25$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Powers (exponents) come before multiplication, division, addition, subtraction
Calculate Powers First: Compute $3^2 = 9$ and $4^2 = 16$ before other operations
Verify Step-by-Step: $81 \div 9 + 16 = 9 + 16 = 25$ ✓

Common Mistakes

Avoid these frequent errors

Performing operations from left to right without considering exponents first
Don't calculate 81÷3 = 27 first, then try 27² + 4² = wrong answer! This ignores the order of operations and creates massive errors. Always calculate all exponents first, then follow PEMDAS strictly.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

Why can't I just work from left to right like in reading?

Mathematics has a specific order that everyone must follow! Without PEMDAS, the same expression could have multiple answers, which would be chaos. Exponents always come before division and addition.

What does the colon symbol (:) mean in this problem?

The colon (:) means division, just like the ÷ symbol. So $81:3^2$ is the same as $81 \div 3^2$ .

How do I remember the order of operations?

Use the acronym PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Many students remember it as "Please Excuse My Dear Aunt Sally."

What if I calculated 81÷3 = 27 first by mistake?

If you get $27^2 + 16 = 729 + 16 = 745$ , that's way too big! Always double-check by following PEMDAS: exponents first gives us $81 \div 9 + 16 = 25$ .

Is there a way to check my final answer?

Yes! Work backwards or use a calculator following PEMDAS. You can also estimate: $81 \div 9$ is about 9, and $4^2 = 16$ , so $9 + 16 = 25$ makes sense!

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