Calculate 10^3: Converting Powers to Integer Form

Power Evaluation with Base Ten

Write the following as an integer:

103= 10^3=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's use the power formula
00:06 Any number (X) to the power of (N)
00:09 equals X multiplied by itself N times
00:19 Let's use this formula in our exercise
00:25 Break down the power into multiplications
00:37 Calculate the multiplications
00:43 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Write the following as an integer:

103= 10^3=

2

Step-by-step solution

To solve the problem of finding 103 10^3 , let us apply the rules of exponents:

  • Step 1: Recognize that 103 10^3 means the base 10 is multiplied by itself three times.
  • Step 2: Write out this multiplication: 10×10×10 10 \times 10 \times 10 .
  • Step 3: Calculate the result step by step.
    First, calculate 10×10=100 10 \times 10 = 100 .
    Next, multiply the result by 10: 100×10=1000 100 \times 10 = 1000 .

Therefore, the expression 103 10^3 evaluates to 1000.

Thus, the solution to this problem is 1000 1000 , which corresponds to choice 4.

3

Final Answer

1000

Key Points to Remember

Essential concepts to master this topic
  • Definition: Exponent shows how many times to multiply the base
  • Technique: 103=10×10×10=1000 10^3 = 10 \times 10 \times 10 = 1000
  • Check: Count zeros: 103 10^3 has 3 zeros after 1 ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying base by exponent instead of using repeated multiplication
    Don't calculate 10 × 3 = 30! This treats the exponent as a multiplier instead of showing repeated multiplication. Always multiply the base by itself the number of times shown by the exponent: 103=10×10×10=1000 10^3 = 10 \times 10 \times 10 = 1000 .

Practice Quiz

Test your knowledge with interactive questions

\( 11^2= \)

FAQ

Everything you need to know about this question

Is there a shortcut for powers of 10?

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Yes! For powers of 10, just write 1 followed by as many zeros as the exponent. So 103 10^3 = 1 with 3 zeros = 1000.

What's the difference between 103 10^3 and 10 × 3?

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103 10^3 means repeated multiplication: 10 × 10 × 10 = 1000. But 10 × 3 is just simple multiplication = 30. The exponent tells you how many times to use 10 as a factor!

How do I remember what exponents mean?

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Think of the exponent as a counter. 103 10^3 means "use 10 as a factor 3 times." Write it out:

  • Factor 1: 10
  • Factor 2: 10
  • Factor 3: 10
Then multiply: 10 × 10 × 10.

Why is 101 10^1 just 10?

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Because 101 10^1 means "use 10 as a factor one time," which is simply 10 itself. Any number to the power of 1 equals that number!

What happens with 100 10^0 ?

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100=1 10^0 = 1 ! This is a special rule: any non-zero number to the power of 0 equals 1. It might seem strange, but it's a fundamental math rule.

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