Question

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Answer 1

Answer:

The value of a = -12

Step-by-step explanation:

Given the equation

$\frac{8^{-55}}{8^a}=8^{-43}$

Determining the value of a

Given the equation

$\frac{8^{-55}}{8^a}=8^{-43}$

Apply the exponent rule:   $\frac{x^a}{x^b}=x^{a-b}$

$\:8^{-55-a}=8^{-43}$   ∵ $\frac{8^{-55}}{8^a}=8^{-55-a}$

$-55-a = -43$

Add 55 to both sides

$-55-a+55=-43+55$

Simplify

$-a=12$

Divide both sides by -1

$\frac{-a}{-1}=\frac{12}{-1}$

Simplify

$a=-12$

Therefore, the value of a = -12