Convert the Expression: Finding the Value of 1/3²

Question

Insert the corresponding expression:

$\frac{1}{3^2}=$

00:00 Simplify the following problem

00:03 According to the laws of exponents, a number raised to the power of (-N)

00:06 equals the reciprocal number raised to the opposite power (N)

00:09 We will apply this formula to our exercise

00:12 We'll convert to the reciprocal number

00:15 and raise to the opposite power (times(-1))

00:18 This is the solution

To solve this problem, we'll use the rule of negative exponents:

Step 1: Identify that the given expression is $\frac{1}{3^2}$ .
Step 2: Recognize that $\frac{1}{3^2}$ can be rewritten using the negative exponent rule.
Step 3: Apply the formula $\frac{1}{a^n} = a^{-n}$ to the expression $\frac{1}{3^2}$ .

Now, let's work through these steps:

Step 1: We have $\frac{1}{3^2}$ where 3 is the base and 2 is the exponent.

Step 2: Using the formula, convert the denominator $3^2$ to $3^{-2}$ .

Step 3: Thus, $\frac{1}{3^2} = 3^{-2}$ .

Therefore, the solution to the problem is $3^{-2}$ .

$3^{-2}$