Final answer:
After simplifying the expressions, options 1, 2, and 4 all equal 1/64, while option 3 equals 64, making it the expression that is not equal to the others.
Step-by-step explanation:
The student's question asks which of the following expressions is not equal to the others: 1) 1/4³, 2) 4²/4⁵, 3) 4⁵/4², 4) 4⁻³. To find the answer, we must analyze each option and simplify the expressions where possible.
For option 1, 1/4³ simplifies to 1/64. For option 2, using the properties of exponents, 4²/4⁵ simplifies to 1/4³ or 1/64. For option 3, 4⁵/4² simplifies to 4³, which equals 64. Lastly, for option 4, 4⁻³ simplifies to 1/4³ or 1/64.
Comparing these, we see that options 1, 2, and 4 are equal because they all simplify to 1/64. However, option 3 is different because it simplifies to 64, not 1/64. Therefore, option 3 is not equal to the others and is the answer to the student's question.