To analyze where Hank made a mistake in solving the equation \(25 = x^4 - 9\), let's go through the steps and check for errors.
The original equation is: \[ 25 = x^4 - 9 \]
Step 1: To get \(x^4\) by itself, we need to add 9 to both sides: \[ 25 + 9 = x^4 \] So, \[ 34 = x^4 \] (Hank made a mistake in this step; he wrote that \(16 = x^4\), which is incorrect.)
Step 2: To solve for \(x\), we need to take the fourth root of both sides: \[ x = \sqrt[4]{34} \] (Hank incorrectly stated \(x=64\). The operation he performed to get to \(64\) is not valid based on the correct calculation.)
Given this evaluation, Hank made a mistake in Step 1 when he incorrectly simplified \(25 + 9\) as \(16\) instead of \(34\).
Thus, the correct response 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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