Question

If n-2 = 1/16, then n could be which of the following?

A.-8
B.-4
C.-1/4
D.1/4
E.4

Answer 1

Option B and E are correct

n could be 4 and -4

Explanation:

Given the following:

`n^(-2) = (1)/(16)`

we know that:

`a^(-n) = (1)/(a^n)`

Then;

`(1)/(n^2)=(1)/(16)`

By cross multiply we have;

`16=n^2`

or

`n^2=16`

⇒
`n = \pm√(16)`

Simplify:

`n =\pm 4`

⇒n = -4 and n = 4

Therefore, n could be 4 and -4

Answer 2

The answer is E.4

The equation is:
`n ^(-2)= (1)/(16)`

Since
`x^(-a)= (1)/( x^(a) )`, then
`n^(-2) = (1)/(n^(2) )`

Therefore, the equation is:

`(1)/( n^(2) ) = (1)/(16)`
⇒
`n^(2) = 16`

`n= √(16)=4`