Simplify the expression. Write your answer as a power. $\left(\left(-3\right)^2\right)^4$((−3)2)4​The simplified expression is

1. Break Down the Problem

We need to simplify the expression $\left((-3)^2\right)^4$, which involves exponents.

2. Relevant Concepts

The relevant exponent rules are:

• $(a^m)^n = a^{m \cdot n}$

3. Analysis and Detail

1. First, evaluate the inner exponent: $(-3)^2 = 9$

2. Next, substitute this value back into the expression: $(9)^4$

3. Now, using the power rule: $(a^m)^n = a^{m \cdot n}$ we can rewrite: $(-3)^{2 \cdot 4} = (-3)^{8}$

4. Verify and Summarize

The simplification steps are valid as they follow the exponentiation rules correctly.

Final Answer

The simplified expression is $(-3)^{8}$.