https://file.aiquickdraw.com/mathbot/file/1726072073005sn4i38sf.jpg

The expression given in the image is:

\[
(2b^4)^3 \times b^6
\]

Let's break this down step by step.

### Step 1: Apply the power of a product rule
For the expression \((2b^4)^3\), we apply the exponent to both the constant \(2\) and the variable \(b^4\):

\[
(2b^4)^3 = 2^3 \times (b^4)^3
\]

Now calculate the powers:
- \(2^3 = 8\)
- \((b^4)^3 = b^{4 \times 3} = b^{12}\)

Thus, the expression simplifies to:

\[
8b^{12}
\]

### Step 2: Multiply by \(b^6\)
Now multiply the result \(8b^{12}\) by \(b^6\):

\[
8b^{12} \times b^6 = 8b^{12+6} = 8b^{18}
\]

### Final Answer:
The simplified expression is:

\[
8b^{18}
\]

Would you like more details or have any questions?

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Here are 5 related questions to deepen your understanding:

1. How would the result change if the original expression was \((2b^5)^3 \times b^7\)?
2. What if you had to simplify \((3x^2)^4 \times x^3\)?
3. Can you find the simplified form of \((4y^3)^2 \times y^5\)?
4. How does the rule of exponents apply when dividing terms with the same base?
5. What if you were given the expression \((ab^2)^4 \times a^3b\)?

**Tip**: Remember that when multiplying powers with the same base, you simply add the exponents!

Learn how to simplify the expression (2b^4)^3 × b^6 using exponentiation rules. This step-by-step solution breaks down the power of a power and the product of powers, ideal for students in Grades 9-12.

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