Question

find the missing factor in exponential form.
$33^9 = 11^9 \cdot \square$
enter the correct answer.

Explanation:

Step1: Recall exponent rule

We know that \(a^n\times b^n=(ab)^n\). So, we can factor \(33\) into its prime factors or into a product of two numbers. Since \(33 = 11\times3\), we can rewrite \(33^9\) using the exponent rule \((ab)^n=a^n\times b^n\).

Step2: Apply the rule

Given \(33^9=(11\times3)^9\). By the exponent rule \((ab)^n = a^n\times b^n\), we have \((11\times3)^9=11^9\times3^9\). Comparing with \(33^9 = 11^9\times\square\), we can see that the missing factor is \(3^9\).

Answer:

\(3^9\)