Numerical Equality: Finding the Expression Equal to 100

Q: Why can't I just multiply the bases together first?

Because exponent rules don't work that way! $ 5^2 \cdot 2^2 $ is NOT the same as $ (5 \cdot 2)^2 $. You can only combine exponents when the bases are the same, like $ 5^2 \cdot 5^3 = 5^5 $.

Q: How do I quickly check if 125 or 64 could equal 100?

Use estimation! Since $ 10^2 = 100 $, any answer much larger (like 125) or smaller (like 64) is clearly wrong. This helps you eliminate wrong choices quickly!

Q: What about the huge number 25⁴?

You don't need to calculate it fully! Since $ 25^2 = 625 $ (much bigger than 100), then $ 25^4 $ will be enormous - definitely not 100.

Q: Is there a pattern to recognize which expressions equal 100?

Yes! Since $ 100 = 10^2 = (2 \cdot 5)^2 = 2^2 \cdot 5^2 $, look for expressions that multiply to give you factors of 4 and 25, like $ 5^2 \cdot 2^2 $.

Q: Should I use a calculator for these problems?

Try mental math first! These are designed to use perfect squares you should know: $ 2^2 = 4 $, $ 4^2 = 16 $, $ 5^2 = 25 $. This builds your number sense!

Exponent Operations with Multiple Base Numbers

Which of the following clauses is equal to 100?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Which of the sections equals 100?

00:06 Let's break down 5 squared

00:09 Let's solve one multiplication at a time and then continue

00:13 This is the solution for the first section

00:17 Let's use the same method for the remaining sections

00:21 This is the solution for the second section

00:26 Let's break down the third section

00:35 This is the solution for the third section

00:38 Let's continue to the fourth section

00:49 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which of the following clauses is equal to 100?

Step-by-step solution

To determine which expression equals 100, we need to evaluate each option:

Option 1: $5^2\cdot5$
- Calculate $5^2 = 25$ .
- Then compute $25 \cdot 5 = 125$ .
Option 2: $4^2\cdot4$
- Calculate $4^2 = 16$ .
- Then compute $16 \cdot 4 = 64$ .
Option 3: $25^4$
- Calculate $(25^4)$ , which simplified through breakdown is larger than 100 because $25^2 = 625$ . Hence this 25 to the power of 4 will definitely be much larger than 100.
Option 4: $5^2\cdot2^2$
- Calculate $5^2 = 25$ .
- Calculate $2^2 = 4$ .
- Compute $25 \cdot 4 = 100$ .

Therefore, the expression in Option 4, $5^2\cdot2^2$ , equals 100. Thus, the correct choice is 4.

Thus, the clause that equals 100 is $5^2\cdot2^2$ .

Final Answer

$5^2\cdot2^2$

Key Points to Remember

Essential concepts to master this topic

Exponents First: Calculate powers before multiplication in order of operations
Technique: $5^2 \cdot 2^2 = 25 \cdot 4 = 100$
Check: Substitute into original expression and verify calculation equals target ✓

Common Mistakes

Avoid these frequent errors

Multiplying before calculating exponents
Don't calculate $5^2 \cdot 2^2$ as $(5 \cdot 2)^2 = 10^2 = 100$ ! This combines bases incorrectly and only works by coincidence. Always calculate each exponent separately first: $5^2 = 25$ , $2^2 = 4$ , then multiply $25 \cdot 4 = 100$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Why can't I just multiply the bases together first?

Because exponent rules don't work that way! $5^2 \cdot 2^2$ is NOT the same as $(5 \cdot 2)^2$ . You can only combine exponents when the bases are the same, like $5^2 \cdot 5^3 = 5^5$ .

How do I quickly check if 125 or 64 could equal 100?

Use estimation! Since $10^2 = 100$ , any answer much larger (like 125) or smaller (like 64) is clearly wrong. This helps you eliminate wrong choices quickly!

What about the huge number 25⁴?

You don't need to calculate it fully! Since $25^2 = 625$ (much bigger than 100), then $25^4$ will be enormous - definitely not 100.

Is there a pattern to recognize which expressions equal 100?

Yes! Since $100 = 10^2 = (2 \cdot 5)^2 = 2^2 \cdot 5^2$ , look for expressions that multiply to give you factors of 4 and 25, like $5^2 \cdot 2^2$ .

Should I use a calculator for these problems?

Try mental math first! These are designed to use perfect squares you should know: $2^2 = 4$ , $4^2 = 16$ , $5^2 = 25$ . This builds your number sense!

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