Question

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

Answer 1

Answer:

The correct choice is

$\boxed{n=4}$

Step-by-step explanation:

The given equation is

$n^{-2}=\frac{1}{16}$

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

$n^{-2}=\frac{1}{4^2}$

Recall that;

$\frac{1}{a^m}=a^{-m}$

We apply this property to obtain;

$n^{-2}=4^{-2}$

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

Therefore $n=4$

Answer 2

Answer:

n = ±4

Step-by-step 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.