Question

question
which expression is equivalent to $3^2 \times 3^{-1}$?

answer
$\frac{1}{27}$ $1$
$3$ $\frac{1}{3}$

Explanation:

Step1: Recall exponent rule

When multiplying exponents with the same base, we use the rule \(a^m\times a^n=a^{m + n}\). Here, the base \(a = 3\), \(m = 2\) and \(n=- 1\).
So, \(3^{2}\times3^{-1}=3^{2+( - 1)}\)

Step2: Simplify the exponent

Calculate the exponent: \(2+( - 1)=2 - 1 = 1\). So the expression becomes \(3^{1}\)

Step3: Evaluate \(3^{1}\)

Any number to the power of 1 is the number itself. So \(3^{1}=3\)

Answer:

3 (corresponding to the option with "3")