Hank is working on simplifying the algebraic expression 4^x−14 when x=5. Her steps are as follows: Step 1: 4^5−14 Step 2: 20−14 Step 3: 6 In which step did Jenny make a mistake? What should she have done differently?

Question

Hank is working on simplifying the algebraic expression 4^x−14 when x=5. Her steps are as follows: Step 1: 4^5−14 Step 2: 20−14 Step 3: 6 In which step did Jenny make a mistake? What should she have done differently?
A) Step 2, Jenny should've added 4 and 5 to get 9.
B) Step 2, Jenny should've calculated the value of 4^5 to be 1,024.
C) Step 3, 20−14 should be 20÷14.
D) Step 1, Jenny should've multiplied 4⋅5 instead of writing 5 as the exponent.

GPT-4o mini · Answer

The correct answer is **B)** Step 2, Jenny should've calculated the value of 4^5 to be 1,024. In her steps, Hank mistakenly calculated 4^5, which does not equal 20. The correct evaluation of 4^5 is 1,024. Therefore, in step 2, instead of arriving at 20, she should have calculated it to be 1,024. The correct simplification would have been 1,024 - 14, which equals 1,010.