Evaluate the Absolute Value Expression: |4 - 3¹| Step-by-Step

Absolute Value with Simple Exponents

431= |4 - 3^1| =

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Step-by-step written solution

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1

Understand the problem

431= |4 - 3^1| =

2

Step-by-step solution

First, calculate 31 3^1 :
31=3 3^1 = 3 .

Then, subtract 3 from 4:
43=1 4 - 3 = 1 .

The absolute value of 1 is 1, so the expression evaluates to 1. Therefore, |4 - 3^1| = 1.

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Evaluate exponents first, then subtract, then absolute value
  • Technique: Calculate 31=3 3^1 = 3 , then 43=1 4 - 3 = 1
  • Check: Since result is positive, absolute value equals the number itself: 1=1 |1| = 1

Common Mistakes

Avoid these frequent errors
  • Applying absolute value before completing operations inside
    Don't find 431=43=1 |4| - |3^1| = 4 - 3 = 1 ! This changes the meaning completely and can give wrong answers when the inside expression is negative. Always evaluate everything inside the absolute value bars first, then apply absolute value to the final result.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

\( \left|18\right|= \)

FAQ

Everything you need to know about this question

Why do I need to calculate the exponent before subtracting?

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The order of operations (PEMDAS) tells us to handle exponents before addition and subtraction. So 31 3^1 must be calculated first to get 3, then we subtract: 43 4 - 3 .

What if the result inside the absolute value bars was negative?

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If we had something like 25 |2 - 5| , we'd get 3=3 |-3| = 3 . The absolute value always gives us the positive distance from zero, so negative results become positive.

Is 31 3^1 really just 3?

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Yes! Any number raised to the power of 1 equals itself. So 31=3 3^1 = 3 , 71=7 7^1 = 7 , etc. It's one of the basic exponent rules.

Can I skip writing the absolute value bars if the answer is positive?

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Never skip steps in your work! Always show that you evaluated what's inside the bars first, then applied the absolute value. This shows your teacher you understand the complete process.

What's the difference between |4 - 3¹| and |4| - |3¹|?

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These are completely different! The first means "find the absolute value of the entire result of 4 - 3¹". The second means "find absolute values separately, then subtract". Always work inside the bars first!

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