Steps to solve:
[tex]\frac{4^-^3}{4^-^1}[/tex]
~Use exponent rule [ [tex]\frac{x^a}{x^b}=x^a^-^b[/tex] ]
[tex]4^-^3^-^(^-^1^)[/tex]
~Simplify
[tex]4^-^2[/tex]
~Use exponent rule [ [tex]a^-^b=\frac{1}{a^b}[/tex] ]
[tex]\frac{1}{4^2}[/tex]
~Simplify
[tex]\frac{1}{16}[/tex]
None of the answer choices show the fully simplified version of the expression but one of the answers will be Option B.
To find the other correct answer, we can check each option.
Option A:
[tex]\frac{4^1}{4^3}[/tex]
~Use exponent rule [ [tex]\frac{x^a}{x^b}=x^a^-^b[/tex] ]
[tex]4^1^-^3[/tex]
~Simplify
[tex]4^-^2[/tex]
~Use exponent rule [ [tex]a^-^b=\frac{1}{a^b}[/tex] ]
[tex]\frac{1}{4^2}[/tex]
~Simplify
[tex]\frac{1}{16}[/tex]
We need to go any further since we found the second correct answer.
Therefore, the answers are Option A and Option B
Best of Luck!
