The expression given in the image is $(2x^9)^3$. Let's solve it step-by-step using the laws of exponents.

Step 1: Apply the power rule for exponents

The power rule states that $(a^m)^n = a^{m \cdot n}$. In this case: $(2x^9)^3 = 2^3 \cdot (x^9)^3$

Step 2: Calculate the exponents separately

• $2^3 = 8$
• $(x^9)^3 = x^{9 \cdot 3} = x^{27}$

Step 3: Combine the results

$(2x^9)^3 = 8x^{27}$

Final Answer

The simplified expression is: $8x^{27}$

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:

1. How would you simplify $(3x^4)^2$?
2. What happens if the base is a negative number in expressions like $(-2x^5)^3$?
3. How can you use the power rule when both exponents are fractions?
4. What is the difference between the power rule and the product rule of exponents?
5. How do you deal with expressions like $(2x^9)^0$?

Tip: Remember that when raising a power to another power, you multiply the exponents.