Question

what is the value of $3^{-1}$?
$3^{-1} = \frac{1}{3}$
what is the value of $3^{-2}$?
$3^{-2} = \frac{1}{9}$
what is the value of $3^{-3}$?
$3^{-3} = $

$3^n$

value

----

----

$3^3$

27

$3^2$

9

$3^1$

3

$3^0$

1

$3^{-1}$

$\frac{1}{3}$

$3^{-2}$

$\frac{1}{9}$

$3^{-3}$

?

Explanation:

Step1: Recall negative exponent rule

For any non-zero base $a$ and positive integer $n$, $a^{-n} = \frac{1}{a^n}$.

Step2: Apply rule to $3^{-3}$

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

Step3: Calculate denominator

$3^3 = 3 \times 3 \times 3 = 27$

Step4: Write final fraction

$3^{-3} = \frac{1}{27}$

Answer:

$\frac{1}{27}$