Answer:
The value of a = -12
Step-by-step explanation:
Given the equation
[tex]\frac{8^{-55}}{8^a}=8^{-43}[/tex]
Determining the value of a
Given the equation
[tex]\frac{8^{-55}}{8^a}=8^{-43}[/tex]
Apply the exponent rule: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]\:8^{-55-a}=8^{-43}[/tex] ∵ [tex]\frac{8^{-55}}{8^a}=8^{-55-a}[/tex]
[tex]-55-a = -43[/tex]
Add 55 to both sides
[tex]-55-a+55=-43+55[/tex]
Simplify
[tex]-a=12[/tex]
Divide both sides by -1
[tex]\frac{-a}{-1}=\frac{12}{-1}[/tex]
Simplify
[tex]a=-12[/tex]
Therefore, the value of a = -12
