Solve 19^-2: Calculating a Specific Negative Exponent

Question

$19^{-2}=\text{?}$

00:00 Solving an exercise with negative exponent

00:03 According to the laws of exponents, any number(A) to the power of(N)

00:06 equals 1 divided by the number(A) to the power of (-N)

00:13 The number(19) becomes 1 divided by(19)

00:15 The exponent(-2) changes its sign to positive -(2-)

00:16 and the exponent(-2) becomes -(-2)

00:19 negative times negative becomes positive so the exponent is 2

00:22 and this is the solution to the question

In order to solve the exercise, we use the negative exponent rule.

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

We apply the rule to the given exercise:

$19^{-2}=\frac{1}{19^2}$

We can then continue and calculate the exponent.

$\frac{1}{19^2}=\frac{1}{361}$

$\frac{1}{361}$