Solve the Basic Multiplication: 10×10 = ?

Multiplication with Exponent Form

Solve the following equation:

10×10= 10\times10=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplify the following problem
00:03 Let's look at possible solutions to the question
00:07 First solution - let's simply calculate
00:10 Now let's look at another solution method
00:14 Any number to the power of 1 is always equal to itself (A)
00:17 Let's apply this formula to our exercise, and raise each number to the power of 1
00:21 According to the laws of exponents, the multiplication of powers with an equal bases (A)
00:25 equals the same base raised to the sum of the exponents (N+M)
00:29 Let's apply this formula to our exercise
00:33 We'll add up the exponents and raise them to this power
00:37 These are the possible solutions to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

10×10= 10\times10=

2

Step-by-step solution

To solve this problem, let’s follow the outlined steps:

  • Step 1: Calculate 10×10 10 \times 10 .
  • Step 2: Express the calculation using exponent rules.
  • Step 3: Verify the possible expressions match the given choices.

Now, let's work through each step:
Step 1: The direct multiplication of 10 by 10 yields 100 100 because 10×10=100 10 \times 10 = 100 .
Step 2: We can express this calculation using the rules of exponents. Since both numbers are 10 and multiplied together: 101×101=101+1=102 10^1 \times 10^1 = 10^{1+1} = 10^2 .
Step 3: We consider the following expressions given in the multiple-choice answers:
- Choice 1: 101+1 10^{1+1} equals 102 10^2 .
- Choice 2: 102 10^2 equals 100.
- Choice 3: 100 is the result of the direct multiplication.

Each choice is consistent with the others through these steps. Thus, all the provided expressions—101+1 10^{1+1} , 102 10^2 , and 100—accurately represent the resolved equation 10×10 10 \times 10 .

Therefore, the solution to the problem is All answers are correct.

3

Final Answer

All answers are correct

Key Points to Remember

Essential concepts to master this topic
  • Rule: Same base multiplication means add the exponents together
  • Technique: Express 10×10 10 \times 10 as 101×101=101+1=102 10^1 \times 10^1 = 10^{1+1} = 10^2
  • Check: Verify all forms equal 100: direct multiplication, exponent notation, and simplified form ✓

Common Mistakes

Avoid these frequent errors
  • Choosing only one correct answer when multiple forms exist
    Don't pick just 100 100 and ignore 102 10^2 = missed equivalent expressions! Each form represents the same value in different notation. Always recognize that 10×10=102=100 10 \times 10 = 10^2 = 100 are all mathematically identical.

Practice Quiz

Test your knowledge with interactive questions

\( (3\times4\times5)^4= \)

FAQ

Everything you need to know about this question

Why are all three answers considered correct?

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All three expressions represent the same mathematical value: 101+1=102=100 10^{1+1} = 10^2 = 100 . They're just written in different forms - exponential notation vs. decimal form!

What does 101+1 10^{1+1} mean exactly?

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101+1 10^{1+1} shows the exponent rule in action: when multiplying same bases, add the exponents. Since 101×101 10^1 \times 10^1 , we get 101+1=102 10^{1+1} = 10^2 .

How do I know when to use exponent form?

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Use exponent form when you're multiplying the same number multiple times. It's especially helpful with powers of 10, like 10×10=102 10 \times 10 = 10^2 or 10×10×10=103 10 \times 10 \times 10 = 10^3 .

Is 102 10^2 always equal to 100?

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Yes! 102 10^2 means 10 squared or 10 × 10, which always equals 100. This is a fundamental fact you should memorize.

What if the question asked for just one answer?

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If forced to choose one, pick the simplest form (usually the number 100). But mathematically, all equivalent expressions are correct answers!

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