Language of Mathematics II (44): Exponents and Radicals (3 of 3)

[MAJESTIcag7]

So 27 with an exponent of 2/3 is really saying the 3rd root of 27 squared?So 27 squared is 279 and yeah...the 3rd root of that would be 9...true indeed...but i don't understand why you didn't have to square it first in order to get to the answer rather than just dealing with the 27 as you did...it all works out in the end i guess but i feel like i'm missing a step...

[chychochycho]

one thing you should try and do most of the time is to take the roots first before squaring them, i.e. make the numbers smaller first before making them bigger. So in this case, take the 3rd root of 27 first then square it. Makes it a lot easier.

[MAJESTIcag7]

@chychochycho Ok..so just treat them as seperate operations instead of lumping them together?

[chychochycho]

yup :)

[lojlomica]

Can you explain the flipping further? I understand how to do the process to solve them but I don't get the idea behind why it works.

[chychochycho]

As far as I know it's just terminology. It's like saying that to the power of 3 means you multiply the object by itself 3 times. We had to come up with a way to send something to the denominator, so we said, let's make it a negative power. That's sort of the way i look at it since i don't know the history behind it, but if i do get a chance i'll try and remember to look it up and if it's interesting, i'll make a video of it :) 

[Johannady]

eh?? that guy doesn't know radicals?? but he is sooo old...

[lienrodeo]

Thankyou again, your work is a priceless resource!

KNOWLEDGE IS POWER......

[mentor32]

Knowledge is indeed power.Thanx again!