Simplify b⁴ × b⁵: Exponent Multiplication Practice

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

Think about what exponents mean! $ b^4 \times b^5 $ means (b·b·b·b) × (b·b·b·b·b). When you multiply, you're combining all the b's together, giving you 9 total b's = $ b^9 $.

Q: What if the bases are different, like a³ × b⁵?

You cannot combine different bases! $ a^3 \times b^5 $ stays as $ a^3b^5 $. The exponent addition rule only works when the bases are exactly the same.

Q: Does this work with negative exponents too?

Yes! The rule works for all exponents. For example: $ b^{-2} \times b^5 = b^{-2+5} = b^3 $. Just add the exponents normally, even if one is negative.

Q: How can I remember this rule?

Think "same base, add the powers!" You can also remember that multiplication means combining all the factors, so you're adding up how many times the base appears total.

Q: What's the difference between b⁴ × b⁵ and (b⁴)⁵?

$ b^4 \times b^5 $ uses the addition rule = $ b^9 $. But $ (b^4)^5 $ uses the power rule where you multiply exponents: $ b^{4 \times 5} = b^{20} $.

Exponent Multiplication with Same Base

Reduce the following equation:

$b^4\times b^5=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's simplify this problem together.

00:09 When multiplying powers with the same base, listen carefully.

00:14 It's the base, A, raised to the power of N plus M.

00:18 Now, let's apply this rule to our problem.

00:23 Keep the base and simply add the exponents.

00:26 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

Reduce the following equation:

$b^4\times b^5=$

Step-by-step solution

To solve this problem, we need to simplify the expression using the rules of exponents:

Step 1: Recognize the base $b$ is the same for both terms in the multiplication.
Step 2: Apply the exponent multiplication rule: add the exponents of like bases. Thus, $b^4 \times b^5 = b^{4+5}$ .

The correct answer to the problem is $b^{4+5}$ .

Final Answer

$b^{4+5}$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying same bases, add the exponents together
Technique: $b^4 \times b^5 = b^{4+5} = b^9$
Check: Count total factors: b·b·b·b × b·b·b·b·b = 9 b's ✓

Common Mistakes

Avoid these frequent errors

Multiplying the exponents instead of adding them
Don't multiply 4 × 5 = 20 to get $b^{20}$ ! This ignores the fundamental rule and creates a completely wrong answer. Always add exponents when multiplying same bases: $b^4 \times b^5 = b^{4+5} = b^9$ .

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I add the exponents instead of multiplying them?

Think about what exponents mean! $b^4 \times b^5$ means (b·b·b·b) × (b·b·b·b·b). When you multiply, you're combining all the b's together, giving you 9 total b's = $b^9$ .

What if the bases are different, like a³ × b⁵?

You cannot combine different bases! $a^3 \times b^5$ stays as $a^3b^5$ . The exponent addition rule only works when the bases are exactly the same.

Does this work with negative exponents too?

Yes! The rule works for all exponents. For example: $b^{-2} \times b^5 = b^{-2+5} = b^3$ . Just add the exponents normally, even if one is negative.

How can I remember this rule?

Think "same base, add the powers!" You can also remember that multiplication means combining all the factors, so you're adding up how many times the base appears total.

What's the difference between b⁴ × b⁵ and (b⁴)⁵?

$b^4 \times b^5$ uses the addition rule = $b^9$ . But $(b^4)^5$ uses the power rule where you multiply exponents: $b^{4 \times 5} = b^{20}$ .

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