Question

find the missing factor in exponential form.
$52^{6} = 13^{6} \cdot \square$
enter the correct answer.

Explanation:

Step1: Recall exponent rule \(a^n \cdot b^n=(ab)^n\)

We know that \(52 = 13\times4\), so \(52^{6}=(13\times4)^{6}\).

Step2: Apply the exponent rule

By the rule \((ab)^n=a^n\cdot b^n\), \((13\times4)^{6}=13^{6}\times4^{6}\).
So comparing with \(52^{6}=13^{6}\cdot\square\), the missing factor is \(4^{6}\).

Answer:

\(4^6\)