Question

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

Answer 1

n = ±4

Explanation:

We have given an equation.

n⁻² = 1 / 16

We have to solve it for n.

The formula for solving this

1/xᵃ = x⁻ᵃ

using this formula in given equation, we have

1 / n² = 1 / 16

since 16 is square of ±4.

1 / n² = 1 / (±4)²

We can write above equation as:

(1/n)² = (1/±4)²

Taking square root to both sides of above equations, we have

1/n= 1/±4

hence, n = ±4 which is the answer.

Answer 2

The correct choice is

`\boxed{n=4}`

Explanation:

The given equation is

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

We rewrite the left hand side of the equation as a power(a number to a given exponent.

`n^(-2)=(1)/(4^2)`

Recall that;

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

We apply this property to obtain;

`n^(-2)=4^(-2)`

Since the exponents are the same, the bases are also the same.

Therefore
`n=4`