Simplify the Expression: b^9 × b^4 × b^5 Using Exponent Rules

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

Because exponents tell you how many times to multiply the base! $ b^9 \times b^4 $ means 9 b's times 4 more b's, giving you 13 total b's, or $ b^{13} $.

Q: What if the bases are different, like $ a^3 \times b^2 $ ?

You cannot combine them! The addition rule only works when the bases are exactly the same. Different bases must stay separate.

Q: Does this work with negative exponents too?

Yes! The rule works for all exponents: positive, negative, fractions, or zero. Just add them normally: $ b^{-2} \times b^5 = b^3 $.

Q: How can I remember this rule?

Think of exponents as counting repeated multiplication. $ b^3 \times b^2 $ means (b×b×b) × (b×b) = b×b×b×b×b = $ b^5 $. You're just counting all the b's!

Q: What about $ (b^3)^2 $ - is that different?

Yes! That uses the power rule where you multiply exponents: $ (b^3)^2 = b^{3×2} = b^6 $. Don't confuse it with the product rule we used here.

Exponent Multiplication with Same Base

Reduce the following equation:

$b^9\times b^4\times b^5=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the following problem

00:04 According to the laws of exponents, the multiplication of exponents with the same base (A)

00:07 equals the same base raised to the sum of the exponents (N+M)

00:11 We will apply this formula to our exercise

00:16 We'll maintain the base and add the exponents together

00:44 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Reduce the following equation:

$b^9\times b^4\times b^5=$

Step-by-step solution

To reduce the equation $b^9 \times b^4 \times b^5$ , follow these steps:

Step 1: Identify the exponents present: $9$ , $4$ , and $5$ .
Step 2: Apply the exponent multiplication rule: Since the bases are the same, add the exponents: $9 + 4 + 5 = 18$ .
Step 3: Write the expression in its simplified form with the new exponent: $b^{18}$ .

Therefore, the simplified form of the expression is $b^{18}$ .

Final Answer

$b^{18}$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying powers with same base, add exponents
Technique: $b^9 \times b^4 \times b^5 = b^{9+4+5} = b^{18}$
Check: Count total factors: 9+4+5=18 base b's multiplied together ✓

Common Mistakes

Avoid these frequent errors

Multiplying the exponents instead of adding them
Don't calculate $b^{9 \times 4 \times 5} = b^{180}$ ! This gives a completely wrong answer because you're confusing multiplication rules with exponent rules. 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 I add the exponents instead of multiplying them?

Because exponents tell you how many times to multiply the base! $b^9 \times b^4$ means 9 b's times 4 more b's, giving you 13 total b's, or $b^{13}$ .

What if the bases are different, like $a^3 \times b^2$ ?

You cannot combine them! The addition rule only works when the bases are exactly the same. Different bases must stay separate.

Does this work with negative exponents too?

Yes! The rule works for all exponents: positive, negative, fractions, or zero. Just add them normally: $b^{-2} \times b^5 = b^3$ .

How can I remember this rule?

Think of exponents as counting repeated multiplication. $b^3 \times b^2$ means (b×b×b) × (b×b) = b×b×b×b×b = $b^5$ . You're just counting all the b's!

What about $(b^3)^2$ - is that different?

Yes! That uses the power rule where you multiply exponents: $(b^3)^2 = b^{3×2} = b^6$ . Don't confuse it with the product rule we used here.

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Simplify the Expression: b^9 × b^4 × b^5 Using Exponent Rules

Exponent Multiplication with Same Base

❤️ 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 the exponents instead of multiplying them?

What if the bases are different, like $a^3 \times b^2$ ?

Does this work with negative exponents too?

How can I remember this rule?

What about $(b^3)^2$ - is that different?

🌟 Unlock Your Math Potential

More Questions

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Simplify the Expression: x^8 × x^7 × x^10 Using Exponent Rules

Simplify the Expression: b^9 × b^4 × b^5 Using Exponent Rules

Exponent Multiplication with Same Base

❤️ 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 the exponents instead of multiplying them?

What if the bases are different, like a3×b2 a^3 \times b^2 a3×b2?

Does this work with negative exponents too?

How can I remember this rule?

What about (b3)2 (b^3)^2 (b3)2 - is that different?

🌟 Unlock Your Math Potential

More Questions

Multiplication of Powers

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

Simplify the Expression: a⁴ × a⁵ × a⁶ Using Exponent Rules

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Simplify the Expression: x^8 × x^7 × x^10 Using Exponent Rules

What if the bases are different, like $a^3 \times b^2$ ?

What about $(b^3)^2$ - is that different?