Solve (7^8)^9: Understanding Nested Power Expressions

Insert the corresponding expression:

$\left(7^8\right)^9=$

To solve this problem, we will apply the exponent rule for power of a power.

Let's go through the solution step-by-step:

• Step 1: Identify the given expression, which is $(7^8)^9$.
• Step 2: Apply the power of a power rule. This rule states that $(a^m)^n = a^{m \times n}$. In this case, $a = 7$, $m = 8$, and $n = 9$.
• Step 3: Calculate $8 \times 9$, which equals 72.
• Step 4: Rewrite the expression using the result: $(7^8)^9 = 7^{72}$.

Therefore, the simplified expression is $7^{72}$.

Looking at the answer choices, the correct choice is:

• Choice 1: $7^{72}$

This choice corresponds exactly with our solution. The other choices do not represent the simplified form of the original expression, making them incorrect.