Solve 5² minus 4¹: Basic Exponent Calculation

Order of Operations with Basic Exponents

Solve the following exercise and circle the correct answer:

52−41= 5^2-4^1=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following expression
00:03 Calculate the exponents
00:10 Continue to solve the expression according to the proper order of operations, from left to right
00:15 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise and circle the correct answer:

52−41= 5^2-4^1=

2

Step-by-step solution

To solve the exercise 52−41= 5^2-4^1= , we need to follow the order of operations, specifically focusing on powers (exponents) before performing subtraction.

  • Step 1: Calculate 52 5^2 . This means we multiply 5 by itself: 5×5=25 5 \times 5 = 25 .

  • Step 2: Calculate 41 4^1 . Any number to the power of 1 is itself, so 41=4 4^1 = 4 .

  • Step 3: Subtract the result of 41 4^1 from 52 5^2 : 25−4 25 - 4 .

  • Step 4: Complete the subtraction: 25−4=21 25 - 4 = 21 .

Thus, the correct answer is 21 21 .

3

Final Answer

21

Key Points to Remember

Essential concepts to master this topic
  • Rule: Calculate exponents before subtraction in order of operations
  • Technique: 52=5×5=25 5^2 = 5 \times 5 = 25 and 41=4 4^1 = 4 , then subtract
  • Check: Substitute back: 25−4=21 25 - 4 = 21 matches the answer ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting before calculating exponents
    Don't calculate 5 - 4 = 1 first = wrong answer of 1 or 9! This ignores the order of operations where exponents come before subtraction. Always calculate 52 5^2 and 41 4^1 first, then subtract.

Practice Quiz

Test your knowledge with interactive questions

\( 11^2= \)

FAQ

Everything you need to know about this question

What does the little number above the 5 and 4 mean?

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That's called an exponent or power! 52 5^2 means "5 to the second power" or "5 squared," which equals 5×5=25 5 \times 5 = 25 .

Why is 41 4^1 just equal to 4?

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Any number to the first power equals itself! This is a basic rule: 41=4 4^1 = 4 , 101=10 10^1 = 10 , 1001=100 100^1 = 100 , and so on.

Do I really need to follow the order of operations for such a simple problem?

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Absolutely! Even simple problems follow the same rules. If you don't calculate exponents first, you'll get completely wrong answers. Good habits start with easy problems!

What if I calculated 5−4=1 5 - 4 = 1 first and then squared it?

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That would give you 12=1 1^2 = 1 , which is totally wrong! The expression 52−41 5^2 - 4^1 means square the 5 first, then subtract 4.

How can I remember the order of operations?

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Use PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Since we have exponents and subtraction here, do exponents first!

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