Question

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Answer 1

The value of a = -12

Explanation:

Given the equation

`(8^(-55))/(8^a)=8^(-43)`

Determining the value of a

Given the equation

`(8^(-55))/(8^a)=8^(-43)`

Apply the exponent rule:
`(x^a)/(x^b)=x^(a-b)`

`\:8^(-55-a)=8^(-43)` ∵
`(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

`(-a)/(-1)=(12)/(-1)`

Simplify

`a=-12`

Therefore, the value of a = -12