To simplify the expression $W^4 \cdot (2W^0W^4)^3$, follow these steps:

Step 1: Simplify $2W^0W^4$

• $W^0 = 1$ (anything raised to the power of 0 is 1).
• So, $2W^0W^4 = 2W^4$.

Step 2: Cube the result

Now calculate $(2W^4)^3$: $(2W^4)^3 = 2^3 \cdot (W^4)^3 = 8W^{12}.$

Step 3: Multiply by $W^4$

The expression becomes: $W^4 \cdot 8W^{12}.$

Using the laws of exponents ($W^a \cdot W^b = W^{a+b}$): $W^4 \cdot W^{12} = W^{16}.$

Thus, the final simplified expression is: $8W^{16}.$

Final Answer:

$8W^{16}$

Would you like further clarification or additional examples?

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Here are five related questions for further exploration:

1. How do you simplify expressions involving exponents with coefficients?
2. What is the significance of $W^0 = 1$?
3. How do you simplify expressions with parentheses raised to a power?
4. What happens when multiplying exponents with different bases?
5. Can this method extend to expressions with fractional exponents?

Tip: Always simplify inside parentheses first before applying exponent rules to avoid mistakes.