Solve the Expression: 4² - 4³ (Exponent Subtraction)

Exponent Evaluation with Negative Results

Solve the following exercise and circle the correct answer:

42−43= 4^2-4^3=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this expression together. Follow along as we go step by step.
00:11 First, focus on the exponents. Break them down carefully.
00:21 Remember, solve all multiplication and division before addition and subtraction.
00:30 Stick to the order of operations, moving from left to right as you go.
00:41 And there you have it! That's the solution. Well done!

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:

42−43= 4^2-4^3=

2

Step-by-step solution

To solve the expression 42−43 4^2 - 4^3 , we start by evaluating each power separately:

  • Calculate 42 4^2 :
    42 4^2 means 4 4 multiplied by itself, which is 4×4=16 4 \times 4 = 16 .

  • Calculate43 4^3 :
    43 4^3 means 4 4 multiplied by itself three times, which is 4×4×4=64 4 \times 4 \times 4 = 64 .

Next, substitute these values back into the expression:

  • 42−43=16−64 4^2 - 4^3 = 16 - 64

Perform the subtraction:

  • 16−64=−48 16 - 64 = -48

Thus, the correct answer is −48-48.

3

Final Answer

-48

Key Points to Remember

Essential concepts to master this topic
  • Rule: Calculate each exponent separately before performing subtraction
  • Technique: 42=16 4^2 = 16 and 43=64 4^3 = 64 , then subtract
  • Check: Verify 16−64=−48 16 - 64 = -48 by adding: −48+64=16 -48 + 64 = 16 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting exponents instead of evaluating them
    Don't calculate 42−3=4−1=14 4^{2-3} = 4^{-1} = \frac{1}{4} ! This treats it like division of powers with the same base, but we need subtraction of the results. Always evaluate each exponent first, then subtract the values.

Practice Quiz

Test your knowledge with interactive questions

\( 11^2= \)

FAQ

Everything you need to know about this question

Why is the answer negative when both exponents are positive?

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The exponents themselves are positive, but we're subtracting the results! Since 43=64 4^3 = 64 is larger than 42=16 4^2 = 16 , we get 16−64=−48 16 - 64 = -48 .

Can I use the rule for subtracting powers with the same base?

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No! The rule am÷an=am−n a^m ÷ a^n = a^{m-n} only works for division, not subtraction. Here we need to calculate each power separately first.

How do I remember the difference between 4² and 4³?

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42 4^2 means 4 × 4 = 16 (square), while 43 4^3 means 4 × 4 × 4 = 64 (cube). The exponent tells you how many 4's to multiply together!

What if I calculated 4³ wrong and got 48 instead of 64?

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That's a common error! 43 4^3 requires three factors: 4×4×4 4 × 4 × 4 . First get 4×4=16 4 × 4 = 16 , then 16×4=64 16 × 4 = 64 .

Should I worry about order of operations here?

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Yes! Follow PEMDAS: calculate the exponents first (42=16 4^2 = 16 and 43=64 4^3 = 64 ), then do the subtraction (16−64 16 - 64 ).

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