Part 2 of 2 Describe and corred the error a student made when starting to solve the equation 8^x+3=2^2x-5 8^x+3=2^2x-5 (2^3)^x+3=2^2x-5 B. The student should have expressed the initial rational exponent as the sum of two rational exponents C. The student should have divided both sides by 2^2 to simplify the expression. D. The student did not convert 8 to the correct power of 2 The comect answer is x=square (Simplify your answer)

The student made an error when converting 8 to the correct power of 2. The correct conversion should be $8 = 2^3$. Therefore, the correct answer is D. The student did not convert 8 to the correct power of 2.<br /><br />To solve the equation $8^{x+3}=2^{2x-5}$, we can rewrite 8 as $2^3$ and then use the property of exponents that states $(a^m)^n = a^{mn}$.<br /><br />So, the equation becomes $(2^3)^{x+3}=2^{2x-5}$.<br /><br />Simplifying the left side, we get $2^{3(x+3)}=2^{2x-5}$.<br /><br />Since the bases are the same, we can set the exponents equal to each other: $3(x+3)=2x-5$.<br /><br />Solving for x, we get $3x+9=2x-5$.<br /><br />Subtracting 2x from both sides, we get $x+9=-5$.<br /><br />Subtracting 9 from both sides, we get $x=-14$.<br /><br />Therefore, the correct answer is $x=-14$.