I am empowered [authorized] to deal with this matter.

我受权处理此事。

《新英汉大辞典》

OK. We'll deal with this matter immediately.

好的。我们将立即处理此事。

youdao

Well, you go back, we discuss how to deal with this matter!

好了，你先回去吧，我们商议下该怎么处理这件事！

youdao

And therefore, approach some sort of unilateral approach to deal with this matter.

NPR: The Future of Sharon's Kadima Party

"I find it particularly disappointing that my predecessor as leader didn't deal with this matter properly through the group rules at the time, " he said.

BBC: David Sprason

Then there was an attempt to try to get a political scalp in the so-called pay-fors that was not a serious attempt to deal with this matter.

WHITEHOUSE: Press Briefing