Solve (20-3×2²)²: Order of Operations and Squaring Practice

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

Order of operations (PEMDAS/BODMAS) is a universal math rule! Working left to right would give different people different answers for the same problem. Following PEMDAS ensures everyone gets the same correct result.

Q: Do I solve the exponent outside the parentheses first?

No! Always solve what's inside parentheses first, no matter what operation comes after. The exponent outside waits until you've completely simplified what's inside the parentheses.

Q: What if I forget to square the final result?

You'll get 8 instead of 64! The outer exponent $ (...)^2 $ applies to the entire simplified expression inside parentheses. Don't forget this final step!

Q: How can I remember the order of operations?

Use the acronym PEMDAS: Please Excuse My Dear Aunt Sally. This helps you remember: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Q: What if there were multiple operations inside the parentheses?

Follow PEMDAS inside the parentheses too! Handle exponents first, then multiplication, then subtraction. The same rules apply everywhere in math.

Order of Operations with Nested Exponents

$(20-3\times2^2)^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Calculate the exponent

00:07 Always solve multiplication and division before addition and subtraction

00:11 Calculate the parentheses and only then square

00:14 Break down and calculate the exponent

00:17 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(20-3\times2^2)^2=$

Step-by-step solution

We begin by solving the expression inside the parentheses $(20-3\times2^2)^2$ . According to the order of operations (PEMDAS/BODMAS), we first handle any calculations inside parentheses and deal with exponents before performing multiplication, division, addition, or subtraction.

Step 1: Solve the exponent inside the parentheses.

2^2

4

$(20-3\times4)^2$

Step 2: Perform the multiplication inside the parentheses.

3

4

12

$(20-12)^2$

Step 3: Perform the subtraction inside the parentheses.

12

20

8

$(8)^2$

Step 4: Finally, solve the remaining exponent.

8^2

64

Thus, $(20-3\times2^2)^2$ equals $64$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then exponents, multiplication, subtraction
Technique: Calculate $2^2 = 4$ , then $3 \times 4 = 12$ , then $20 - 12 = 8$
Check: Substitute final result: $8^2 = 64$ matches our answer ✓

Common Mistakes

Avoid these frequent errors

Solving operations left to right without following PEMDAS
Don't work left to right like (20-3)×2² = 17×4 = 68, then 68² = 4624! This ignores order of operations and gives wrong answers. Always handle exponents before multiplication, and operations inside parentheses before squaring the result.

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?

Order of operations (PEMDAS/BODMAS) is a universal math rule! Working left to right would give different people different answers for the same problem. Following PEMDAS ensures everyone gets the same correct result.

Do I solve the exponent outside the parentheses first?

No! Always solve what's inside parentheses first, no matter what operation comes after. The exponent outside waits until you've completely simplified what's inside the parentheses.

What if I forget to square the final result?

You'll get 8 instead of 64! The outer exponent $(...)^2$ applies to the entire simplified expression inside parentheses. Don't forget this final step!

How can I remember the order of operations?

Use the acronym PEMDAS: Please Excuse My Dear Aunt Sally. This helps you remember: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

What if there were multiple operations inside the parentheses?

Follow PEMDAS inside the parentheses too! Handle exponents first, then multiplication, then subtraction. The same rules apply everywhere in math.

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