A2 1-2 Rational Exponents and p Properties of Exponents Describe and coned the entor a student made when starting to solve the equition e^x+3+2^2x-3 A. The student did eat distribute ) in (2^3)^n+2 across x=1 B. The stuant shmat have 7. to smelly the expression not convert D.to the comed pount of 2

## Step 1<br />The problem presents an equation \(e^{x+3}+2^{2x-3}\) and asks us to identify the mistake a student might make while solving it. The options provided are:<br />A. The student did not distribute 3 in \((2^{3})^{n+2}\) across \(x=1\)<br />B. The student did not convert 2 to the correct power of 2<br />C. The student did not divide both sides of the equation by the expression<br /><br />## Step 2<br />We need to analyze each option to see which one is the most likely mistake a student could make.<br /><br />## Step 3<br />Option A suggests that the student did not distribute 3 in \((2^{3})^{n+2}\) across \(x=1\). However, this is not a valid mistake because the equation does not contain \((2^{3})^{n+2}\).<br /><br />## Step 4<br />Option B suggests that the student did not convert 2 to the correct power of 2. This is a valid mistake because the equation contains \(2^{2x-3}\), which means that 2 should be raised to the power of \(2x-3\).<br /><br />## Step 5<br />Option C suggests that the student did not divide both sides of the equation by the expression. This is not a valid mistake because the equation does not require division by an expression.