Let's analyze Hank's work step by step.
The original equation is:
\[ 25 = x^4 - 9 \]
Step 1: Hank indicates that he moved to:
\[ 16 = x^4 \]
To check this, we should add 9 to both sides of the equation to isolate \(x^4\):
\[ 25 + 9 = x^4 \]
This simplifies to:
\[ 34 = x^4 \]
So, Hank made a mistake in Step 1. He incorrectly subtracted 9 instead of adding 9.
Step 2: In his work, Hank then solved for \(x\) by stating:
\[ x = 64 \]
This is incorrect because the previous result of \(x^4\) was incorrect. From the correct equation \(34 = x^4\), he should take the fourth root of \(34\) to find \(x\).
Thus, the correct identification of Hank's mistake is:
Hank made a mistake in Step 1. The first step needed to solve this correctly would be to add 9 to both sides of the equation. Hank subtracted 9 instead of adding 9.
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