Simplify the Expression: a³ · a² · b⁴ · b⁵ Using Exponent Rules

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

Because $ a^3 $ means a × a × a, and $ a^2 $ means a × a. When you multiply them together, you get a × a × a × a × a = $ a^5 $. You're counting the total number of a's!

Q: What if the bases are different like a and b?

Different bases stay separate! You can only add exponents when the bases are identical. So $ a^3 \cdot b^4 $ stays as $ a^3b^4 $ - don't try to combine them.

Q: Can I simplify this expression further?

No, $ a^5b^9 $ is fully simplified! Since a and b are different variables, they cannot be combined any further. This is your final answer.

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

Use addition when multiplying same bases: $ a^3 \cdot a^2 = a^{3+2} $. Use multiplication when raising a power to a power: $ (a^3)^2 = a^{3 \times 2} $. These are completely different rules!

Q: How do I remember which operation to use?

Think of it as counting! When multiplying $ a^3 \cdot a^2 $, you're counting how many a's total: 3 + 2 = 5. So the rule is multiplication → addition.

Exponent Rules with Multiple Base Terms

Simplify the expression:

$a^3\cdot a^2\cdot b^4\cdot b^5=$

❤️ 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

00:10 Alright, let's simplify this together.

00:13 We'll use the formula for multiplying powers. Here's how it works:

00:18 When you multiply a number, A, raised to the M, with the same number, A, raised to the N,

00:24 it equals the number, A, raised to the power of M plus N.

00:30 Let's apply this rule to our problem!

00:33 We'll combine the powers with the same base. And there you go!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the expression:

$a^3\cdot a^2\cdot b^4\cdot b^5=$

Step-by-step solution

In the exercise of multiplying powers, we will add up all the powers of the same product, in this case the terms a, b

We use the formula:

$a^n\times a^m=a^{n+m}$

We are going to focus on the term a:

$a^3\times a^2=a^{3+2}=a^5$

We are going to focus on the term b:

$b^4\times b^5=b^{4+5}=b^9$

Therefore, the exercise that will be obtained after simplification is:

$a^5\times b^9$

Final Answer

$a^5\cdot b^9$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying same bases, add the exponents together
Technique: Group like bases: $a^3 \cdot a^2 = a^{3+2} = a^5$
Check: Count total exponents: 3+2=5 for a, 4+5=9 for b ✓

Common Mistakes

Avoid these frequent errors

Multiplying exponents instead of adding them
Don't multiply exponents like $a^3 \cdot a^2 = a^6$ or $b^4 \cdot b^5 = b^{20}$ ! This gives completely wrong answers because you're using multiplication rules instead of exponent rules. Always add exponents when multiplying same bases: $a^3 \cdot a^2 = a^{3+2} = a^5$ .

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why do I add exponents instead of multiplying them?

Because $a^3$ means a × a × a, and $a^2$ means a × a. When you multiply them together, you get a × a × a × a × a = $a^5$ . You're counting the total number of a's!

What if the bases are different like a and b?

Different bases stay separate! You can only add exponents when the bases are identical. So $a^3 \cdot b^4$ stays as $a^3b^4$ - don't try to combine them.

Can I simplify this expression further?

No, $a^5b^9$ is fully simplified! Since a and b are different variables, they cannot be combined any further. This is your final answer.

What's the difference between adding and multiplying exponents?

Use addition when multiplying same bases: $a^3 \cdot a^2 = a^{3+2}$ . Use multiplication when raising a power to a power: $(a^3)^2 = a^{3 \times 2}$ . These are completely different rules!

How do I remember which operation to use?

Think of it as counting! When multiplying $a^3 \cdot a^2$ , you're counting how many a's total: 3 + 2 = 5. So the rule is multiplication → addition.

🌟 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

Simplify the Expression: a³ · a² · b⁴ · b⁵ Using Exponent Rules

Exponent Rules with Multiple Base Terms

❤️ 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 add exponents instead of multiplying them?

What if the bases are different like a and b?

Can I simplify this expression further?

What's the difference between adding and multiplying exponents?

How do I remember which operation to use?

🌟 Unlock Your Math Potential

More Questions

Applying Combined Exponents Rules

Simplify the Expression: k²·t⁴·k⁶·t² Using Exponent Rules

Simplify the Expression: c^(-1)·d^6·d^(-2)·c^3·c^2 Using Laws of Exponents

Solve: 10·10²·10⁻⁴·10¹⁰ Using Powers of 10

Solve: a²÷a + a³×a⁵ Expression Using Laws of Exponents

Multiplication of Powers

Simplify the Expression: a·b·a·b·a² Using Exponent Rules

Simplify the Expression: a²×2a³×3a⁻¹ Using Exponent Rules

Simplify the Expression: 2^10 × 2^7 × 2^6 Using Laws of Exponents

Multiply Powers with Same Base: Calculate 8²⋅8³⋅8⁵

Exponents Rules

Simplify E⁶·F⁻⁴·E⁰·F⁷·E: Multiple Exponent Operations

Simplify the Exponential Product: 3^x ⋅ 2^x ⋅ 3^(2x)

Simplify the Expression: 5^-3 × 5^0 × 5^2 × 5^5 Using Laws of Exponents

Simplify the Expression: Y² + Y⁶ - Y⁵Y Polynomial Problem