Simplify 13³ × 13⁴ × 13²: Multiplying Powers with Same Base

Q: Why do we add exponents instead of multiplying them?

Because exponents represent repeated multiplication! $ 13^3 $ means 13 × 13 × 13, so when you multiply $ 13^3 \times 13^4 $, you're combining all those 13's together.

Q: What happens to the base number?

The base stays exactly the same! Only the exponents change. In $ 13^3 \times 13^4 \times 13^2 $, the base 13 remains 13 in our final answer.

Q: Can I use this rule with different bases?

No! This rule only works when the bases are identical. For example, $ 13^3 \times 14^4 $ cannot be simplified using this rule because 13 ≠ 14.

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

Think: Same base = Add exponents when multiplying. Different operations like $ (13^3)^4 $ use different rules where you'd multiply exponents.

Q: What if one of the exponents is 1 or 0?

Just add normally! $ 13^1 = 13 $ and $ 13^0 = 1 $. So $ 13^3 \times 13^1 \times 13^0 = 13^{3+1+0} = 13^4 $.

Exponent Rules with Multiple Powers

Simplify the following equation:

$13^3\times13^4\times13^2=$

❤️ 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 simplify this problem step by step.

00:12 Remember, when multiplying exponents with the same base, like A,

00:17 the result is the same base raised to the power of N plus M.

00:22 Now, we'll use this formula in our exercise.

00:25 Keep the base the same, and simply add together the exponents.

00:38 And that gives us the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the following equation:

$13^3\times13^4\times13^2=$

Step-by-step solution

We need to simplify the expression $13^3 \times 13^4 \times 13^2$ .

To do this, we'll use the multiplication rule for exponents, which states that when multiplying powers with the same base, we add the exponents. Mathematically, $a^m \times a^n = a^{m+n}$ . Here, the common base is 13.

Let's apply this rule:

The given expression is $13^3 \times 13^4 \times 13^2$ .
Using the rule, we add the exponents together: $3 + 4 + 2$ .
Calculate the total exponent: $3 + 4 + 2 = 9$ .

Therefore, the simplified expression is $13^9$ .

So, the solution to the problem is $13^9$ .

Final Answer

$13^9$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying powers with same base, add the exponents
Technique: For $13^3 \times 13^4 \times 13^2$ , calculate 3 + 4 + 2 = 9
Check: Verify base stays same: $13^9$ has base 13 ✓

Common Mistakes

Avoid these frequent errors

Multiplying the exponents instead of adding them
Don't multiply 3 × 4 × 2 = 24 to get $13^{24}$ ! This confuses the power rule with multiplication rule. Always add exponents when multiplying powers with the same base.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why do we add exponents instead of multiplying them?

Because exponents represent repeated multiplication! $13^3$ means 13 × 13 × 13, so when you multiply $13^3 \times 13^4$ , you're combining all those 13's together.

What happens to the base number?

The base stays exactly the same! Only the exponents change. In $13^3 \times 13^4 \times 13^2$ , the base 13 remains 13 in our final answer.

Can I use this rule with different bases?

No! This rule only works when the bases are identical. For example, $13^3 \times 14^4$ cannot be simplified using this rule because 13 ≠ 14.

How do I remember when to add versus multiply exponents?

Think: Same base = Add exponents when multiplying. Different operations like $(13^3)^4$ use different rules where you'd multiply exponents.

What if one of the exponents is 1 or 0?

Just add normally! $13^1 = 13$ and $13^0 = 1$ . So $13^3 \times 13^1 \times 13^0 = 13^{3+1+0} = 13^4$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Exponents Rules 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