Radtional Number Exponents

[lolily]

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]

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]

You do know that 125 = 5^3 and 64 = 4^3, right?

 

[lolily]

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