Step-by-step explanation:
[tex](36^{5} - 6^{9})(38^{9} - 38^{8})[/tex]
First, let's change the [tex]36[/tex] to have the same based as the other exponential in its parenthesis:
[tex]((6^{2})^{5} - 6^{9})(38^{9} - 38^{8})[/tex]
[tex](6^{10} - 6^{9})(38^{9} - 38^{8})[/tex]
Next, we can factor out a [tex]6^{9}[/tex] in the first set of parentheses:
[tex](6^{9}(6^{1} - 1))(38^{9} - 38^{8})[/tex]
[tex](6^{9} * 5)(38^{9} - 38^{8})[/tex]
Next, we can factor out a [tex]38^{8}[/tex] in the second set of parentheses:
[tex](6^{9} * 5)(38^{8} (38^{1} - 1)[/tex]
[tex](6^{9} * 5)(38^{8} * 37)[/tex]
Finally, we can multiply one of the [tex]6[/tex]s from the first parentheses with the [tex]5[/tex] to get [tex]30[/tex]:
[tex](6^{8} * 30)(38^{8} * 37)[/tex]
Rewriting this shows that the result of the original problem will have a factor of [tex]30[/tex] and [tex]37[/tex]:
[tex]6^{8} * 38^{8} * 30 * 37[/tex]
