Solve 64÷2³+5²: Order of Operations Challenge

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

Mathematics has a special order called PEMDAS (or BODMAS) that ensures everyone gets the same answer. If we worked left to right, $ 64÷2^3+5^2 $ would give different results depending on how you read it!

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

The colon (:) means division, just like the ÷ symbol. So $ 64:2^3 $ is the same as $ 64÷2^3 $.

Q: How do I remember which operations come first?

Use PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Think "Please Excuse My Dear Aunt Sally!"

Order of Operations with Exponents and Division

$64:2^3+5^2=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$64:2^3+5^2=$

Step-by-step solution

First, calculate the powers:

$2^3 = 8$

$5^2 = 25$

Now substitute these values into the expression:

$64:2^3+5^2 = 64:8+25$

Perform the division:

$64 \div 8 = 8$

Finally, add the result to 25:

$8 + 25 = 33$

Final Answer

$33$

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate exponents first, then division, finally addition
Technique: $2^3 = 8$ and $5^2 = 25$ before any other operations
Check: Work backwards: 33 - 25 = 8, and 8 × 8 = 64 ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following order of operations
Don't calculate 64÷2 = 32 first, then 32³ + 5² = massive wrong answer! This ignores the fact that exponents come before division. Always calculate all exponents first (2³ = 8, 5² = 25), then division (64÷8 = 8), then addition (8 + 25 = 33).

Practice Quiz

Test your knowledge with interactive questions

$5+\sqrt{36}-1=$

FAQ

Everything you need to know about this question

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

Mathematics has a special order called PEMDAS (or BODMAS) that ensures everyone gets the same answer. If we worked left to right, $64÷2^3+5^2$ would give different results depending on how you read it!

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

The colon (:) means division, just like the ÷ symbol. So $64:2^3$ is the same as $64÷2^3$ .

How do I remember which operations come first?

Use PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Think "Please Excuse My Dear Aunt Sally!"

What if I got 13 or 39 as my answer?

You likely made an order error! 13 comes from adding first (64÷(2³+5²) = 64÷33), and 39 comes from calculating 64÷2 = 32 first. Remember: exponents always come before division and addition.

Is there a way to check my answer without redoing the whole problem?

Yes! Work backwards: start with 33, subtract 25 to get 8, then check if 64÷8 = 8. Also verify that $2^3 = 8$ and $5^2 = 25$ .

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