Let's break this down.

We are given:

\[
(i^4)^{2.25} = i^9
\]

We know the properties of exponents:

\[
(a^m)^n = a^{m \cdot n}
\]

### Step 1: Simplify the left-hand side
Using this exponent rule on \( (i^4)^{2.25} \):

\[
(i^4)^{2.25} = i^{4 \cdot 2.25} = i^9
\]

### Step 2: Compare both sides
We now see that both sides of the equation simplify to \( i^9 \), so the equation holds true.

Therefore, the statement is correct:

\[
(i^4)^{2.25} = i^9
\]

Would you like further details or have any questions?

### Follow-up questions:
1. What are the properties of complex numbers like \( i \)?
2. How do exponent rules apply to complex numbers?
3. Can you provide more examples of simplifying exponents involving imaginary numbers?
4. What is the value of \( i^9 \)?
5. How do we calculate powers of \( i \) systematically?

**Tip**: The powers of \( i \) cycle every 4 terms: \( i^1 = i \), \( i^2 = -1 \), \( i^3 = -i \), \( i^4 = 1 \).

Learn how to simplify complex exponentiation with the equation (i^4)^2.25 = i^9. This problem uses key concepts such as exponentiation rules and the cyclical powers of the imaginary unit i. Suitable for students in Grades 9-12.

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