Radtional Number Exponents

lolily

New member
Joined
Jan 28, 2019
Messages
7
Hi! So, I'm stuck on figuring out how to simplify problems that look like this: (-64/125)^(-2/3). The answer listed in the back of the textbook is 25/16. I had previously tried to solve by expanding the problem into (1/-64/125)^(2/3), and then (1^2/3)/(-64^2/3)/125^2/3) but needless to say that was wrong. Is there anyone who knows a list of steps to complete this problem so I will be able to work through them on my own? Thanks so much in advance, I really appreciate the help.
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,790
Hi! So, I'm stuck on figuring out how to simplify problems that look like this: (-64/125)^(-2/3). The answer listed in the back of the textbook is 25/16. I had previously tried to solve by expanding the problem into (1/-64/125)^(2/3), and then (1^2/3)/(-64^2/3)/125^2/3) but needless to say that was wrong. Is there anyone who knows a list of steps to complete this problem so I will be able to work through them on my own? Thanks so much in advance, I really appreciate the help.
Personally, I would ALWAYS do this, first: \(\displaystyle \left(-\dfrac{64}{125}\right)^{-2/3} = \left(-\dfrac{125}{64}\right)^{2/3}\)

A good second step might be the complete factorization of the 125 and the 64. I'll leave the details to you.
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,480
You do know that 125 = 5^3 and 64 = 4^3, right?
 

lolily

New member
Joined
Jan 28, 2019
Messages
7
You do know that 125 = 5^3 and 64 = 4^3, right?
Yes! I just overthought it and confused myself completely. Haha. Thanks for the help, guys
 
Top