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!