Simplify the Expression: 12×12² Step-by-Step Solution

Q: Why do I need to write 12 as $ 12^1 $ ?

Writing 12 as $ 12^1 $ helps you see the pattern clearly! Any number without an exponent actually has an invisible exponent of 1, so $ 12 = 12^1 $.

Q: What's the difference between adding and multiplying exponents?

Add exponents when multiplying same bases: $ 12^1 \times 12^2 = 12^{1+2} $. Multiply exponents when raising a power to a power: $ (12^2)^3 = 12^{2×3} $.

Q: Can I just calculate $ 12 \times 12^2 $ directly?

Yes! $ 12 \times 144 = 1728 $ works, but using exponent rules is much faster for larger numbers and helps you understand the mathematical pattern.

Q: How do I remember when to add vs multiply exponents?

Think of it this way: Same base, different operation. Multiplying bases → add exponents. Taking a power to a power → multiply exponents. The operation tells you what to do!

Q: What if the bases were different numbers?

If bases are different (like $ 5^2 \times 3^4 $), you cannot combine the exponents. The rule only works when the bases are exactly the same.

Exponent Rules with Same Base Multiplication

Simplify the following equation:

$12\times12^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's simplify this problem together.

00:09 Remember, any number to the power of one is just that number.

00:13 Let's use this rule in our exercise.

00:18 When you multiply powers with the same base, like A,

00:23 You keep the base and add the powers together, like N plus M.

00:28 We're going to apply this formula now.

00:32 So, we'll add the powers and raise it.

00:35 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the following equation:

$12\times12^2=$

Step-by-step solution

To simplify the equation $12 \times 12^2$ , follow these steps:

Step 1: Recognize that 12 can be expressed as a power. Since $12 = 12^1$ , rewrite the equation as $12^1 \times 12^2$ .
Step 2: Apply the rule for multiplying powers with the same base, which states that $a^m \times a^n = a^{m+n}$ . In this case, this becomes $12^{1+2}$ .
Step 3: Simplify the expression by adding the exponents: $1 + 2 = 3$ .

Thus, the simplified form of the expression is $12^3$ .

Therefore, the correct answer choice is $12^{1+2}$ , which corresponds to choice 2.

Final Answer

$12^{1+2}$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying same bases, add the exponents: $a^m \times a^n = a^{m+n}$
Technique: Convert 12 to $12^1$ , then $12^1 \times 12^2 = 12^{1+2}$
Check: Verify by calculating both ways: $12 \times 144 = 1728$ and $12^3 = 1728$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying the exponents instead of adding them
Don't multiply 1 × 2 = 2 to get $12^2$ = wrong answer 144! This confuses the power rule with multiplication rule. Always add exponents when multiplying same bases: $12^1 \times 12^2 = 12^{1+2} = 12^3$ .

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I need to write 12 as $12^1$ ?

Writing 12 as $12^1$ helps you see the pattern clearly! Any number without an exponent actually has an invisible exponent of 1, so $12 = 12^1$ .

What's the difference between adding and multiplying exponents?

Add exponents when multiplying same bases: $12^1 \times 12^2 = 12^{1+2}$ . Multiply exponents when raising a power to a power: $(12^2)^3 = 12^{2×3}$ .

Can I just calculate $12 \times 12^2$ directly?

Yes! $12 \times 144 = 1728$ works, but using exponent rules is much faster for larger numbers and helps you understand the mathematical pattern.

How do I remember when to add vs multiply exponents?

Think of it this way: Same base, different operation. Multiplying bases → add exponents. Taking a power to a power → multiply exponents. The operation tells you what to do!

What if the bases were different numbers?

If bases are different (like $5^2 \times 3^4$ ), you cannot combine the exponents. The rule only works when the bases are exactly the same.

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Simplify the Expression: 12×12² Step-by-Step Solution

Exponent Rules with Same Base Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to write 12 as $12^1$ ?

What's the difference between adding and multiplying exponents?

Can I just calculate $12 \times 12^2$ directly?

How do I remember when to add vs multiply exponents?

What if the bases were different numbers?

🌟 Unlock Your Math Potential

More Questions

Multiplication of Powers

Simplify 7^6 × 7^6: Exponent Multiplication Practice

Simplify 11^10 × 11^11: Multiplying Powers with Same Base

Simplify 6^2 × 6^8: Product Rule of Exponents Practice

Simplify the Expression: 8³ × 8 Using Exponent Rules

Simplify the Expression: 12×12² Step-by-Step Solution

Exponent Rules with Same Base Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to write 12 as 121 12^1 121?

What's the difference between adding and multiplying exponents?

Can I just calculate 12×122 12 \times 12^2 12×122 directly?

How do I remember when to add vs multiply exponents?

What if the bases were different numbers?

🌟 Unlock Your Math Potential

More Questions

Multiplication of Powers

Simplify 7^6 × 7^6: Exponent Multiplication Practice

Simplify 11^10 × 11^11: Multiplying Powers with Same Base

Simplify 6^2 × 6^8: Product Rule of Exponents Practice

Simplify the Expression: 8³ × 8 Using Exponent Rules

Why do I need to write 12 as $12^1$ ?

Can I just calculate $12 \times 12^2$ directly?