Solve 20-3³÷3: Order of Operations Challenge

Order of Operations with Exponents

2033:3= 20-3^3:3=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

2033:3= 20-3^3:3=

2

Step-by-step solution

First, compute the power: 33=27 3^3 = 27 .

Next, divide: 27÷3=9 27 \div 3 = 9 .

Finally, subtract: 209=11 20 - 9 = 11 .

3

Final Answer

11 11

Key Points to Remember

Essential concepts to master this topic
  • Rule: Follow PEMDAS - exponents before division before subtraction
  • Technique: Calculate 33=27 3^3 = 27 , then 27÷3=9 27 ÷ 3 = 9 , finally 209 20 - 9
  • Check: Work left to right after exponents: 2033÷3=209=11 20 - 3^3 ÷ 3 = 20 - 9 = 11

Common Mistakes

Avoid these frequent errors
  • Working strictly left to right without considering order of operations
    Don't calculate 20 - 3 = 17 first, then cube and divide = wrong answer like 26! This ignores that exponents and division come before subtraction. Always follow PEMDAS: calculate 33 3^3 first, then divide by 3, then subtract from 20.

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 reading?

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Math has a special order called PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). This ensures everyone gets the same answer! Working left to right would give different results for the same problem.

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

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The colon (:) means division, just like the ÷ symbol. So 33:3 3^3:3 is the same as 33÷3 3^3 ÷ 3 or 333 \frac{3^3}{3} .

How do I remember to do exponents first?

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Think of PEMDAS as "Please Excuse My Dear Aunt Sally." The E (Exponents) comes before M/D (Multiplication/Division) and A/S (Addition/Subtraction).

What if I calculated 203=17 20 - 3 = 17 first?

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That's a common mistake! If you get 173÷3=4913÷3=163723 17^3 ÷ 3 = 4913 ÷ 3 = 1637\frac{2}{3} , you know something's wrong. Always handle exponents before any other operations.

Is there a way to check my answer?

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Yes! Work through the problem step-by-step again, or use a calculator following order of operations. You should get 11 both ways if you're doing it correctly.

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