Saturday, June 17, 2023

figure it out

This one's easy, but I admit I did it on paper:

My answer will be in the comments section.



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Posted by Kevin Kim at 6/17/2023 10:37:00 PM

1 comment:

Kevin Kim said...

The initial problem to solve is:

[(6^7+6^7+6^7+6^7+6^7)/(5^7+5^7+5^7+5^7+5^7+5^7+5^7)]^(1/6)

Right away, we see the numerator can be rewritten as

5(6^7), and the denominator becomes

6(5^7)

So the problem becomes

[5(6^7)/6(5^7)]^1/6

Inside the fraction, the 5 on top is canceled by the 5^7 on the bottom, and the 6 on the bottom is canceled by the 6^7 on the top, leaving you with

(6^6/5^6)^(1/6)

So the sixth root of (6^6/5^6) is just

6/5.

QED.

June 17, 2023 at 10:49:00 PM GMT+9

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