Here is a question I did when learning algebra thorugh the AoPS Intro to Algebra TEXTBOOK
Don't worry, this is from the textbook I'm self-learning and I've solved it.
This is also from an AMC12 so it's not a violation of copyright since I'm citing it
It's good for a exponent refresher.
Latex isn't working so here's the photo.
This should be relatively easy for the moderators and probably some of the regular users too
I did it in 3 minutes, my parents in like 30 seconds LOL
_________________ = ____
5^(26/x) * 25^(17/x) 25^2
5^(48/x - 26/x) 1
_____________ = ______
5^( 22/x) 1
_______ = ________
_______ = _____
Which implies that 12/x = 4 ⇒ x = 3
THis is how I did it(or similar, this is from a few days ago, doing it now)
So we first convert all 25^whatevers into 5^somethings
5^-4 = 5^48/x OVER 5^26/x * 5*34/x = 5 ^(48-26-34)x = 5^-12x
so -12x = -4, x = 3
essentially the same as what you did
And also I'd nominate your answer for "Best Answer"