Calculate 5×5×5×2×2×2: Product of Repeated Multiplication

Q: Why should I group the factors instead of multiplying left to right?

Strategic grouping makes calculations much easier! Pairing 5×2=10 gives you nice round numbers. Computing $ 10^3 = 1000 $ is simpler than $ 125 \times 8 $.

Q: Can I group the factors in any order I want?

Yes! The commutative property lets you multiply in any order. Try grouping to make round numbers like 10, 100, or other easy multiples.

Q: What if I can't see an easy grouping pattern?

Look for factors that multiply to give powers of 10 (like 2×5=10). If that doesn't work, try grouping identical numbers together: $ 5^3 \times 2^3 $.

Q: How do I check if 1000 is the right answer?

Calculate it a different way! Try $ 5^3 \times 2^3 = 125 \times 8 $. You can also break down: $ 125 \times 8 = 125 \times (10-2) = 1250-250 = 1000 $ ✓

Q: Is there a shortcut for problems like this?

Yes! When you see repeated factors, look for exponent patterns. Here: $ 5^3 \times 2^3 = (5 \times 2)^3 = 10^3 = 1000 $

Exponent Multiplication with Strategic Grouping

$5\cdot5\cdot5\cdot2\cdot2\cdot2=?$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve the problem together!

00:11 First, we'll rearrange the equation to make it simpler.

00:16 Next, we'll tackle each multiplication step by step. Ready? Let's go!

00:27 Great job! We'll continue solving using the same steps.

00:32 And there you have it! That's our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5\cdot5\cdot5\cdot2\cdot2\cdot2=?$

Step-by-step solution

We use the substitution property and organize the exercise in the following order:

$5\times2\times5\times2\times5\times2=$

We place parentheses in the exercise:

$(5\times2)\times(5\times2)\times(5\times2)=$

We solve from left to right:

$10\times10\times10=$

$(10\times10)\times10=$

$100\times10=1000$

Final Answer

1000

Key Points to Remember

Essential concepts to master this topic

Property: Use commutative property to rearrange factors efficiently
Technique: Group equal bases: (5×2)×(5×2)×(5×2) = 10×10×10
Check: Verify by computing step-by-step: 125×8 = 1000 ✓

Common Mistakes

Avoid these frequent errors

Computing factors sequentially without grouping
Don't calculate 5×5×5×2×2×2 = 125×8 directly! This makes mental math harder and increases error risk. Always group equal pairs first: (5×2)³ = 10³ = 1000 for easier calculation.

Practice Quiz

Test your knowledge with interactive questions

$74+32+6+4+4=\text{?}$

FAQ

Everything you need to know about this question

Why should I group the factors instead of multiplying left to right?

Strategic grouping makes calculations much easier! Pairing 5×2=10 gives you nice round numbers. Computing $10^3 = 1000$ is simpler than $125 \times 8$ .

Can I group the factors in any order I want?

Yes! The commutative property lets you multiply in any order. Try grouping to make round numbers like 10, 100, or other easy multiples.

What if I can't see an easy grouping pattern?

Look for factors that multiply to give powers of 10 (like 2×5=10). If that doesn't work, try grouping identical numbers together: $5^3 \times 2^3$ .

How do I check if 1000 is the right answer?

Calculate it a different way! Try $5^3 \times 2^3 = 125 \times 8$ . You can also break down: $125 \times 8 = 125 \times (10-2) = 1250-250 = 1000$ ✓

Is there a shortcut for problems like this?

Yes! When you see repeated factors, look for exponent patterns. Here: $5^3 \times 2^3 = (5 \times 2)^3 = 10^3 = 1000$

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime