exponents

[RachelB]

I have one problem that I am stuck on. I know it should be easy but I AM DOING SOMETHING WRONGE. Please help.

40. (-125) -2/3

The direction say evaluate the expression without using a calculater.

 

[jonboy]

I assume you mean:\(\displaystyle \L \;(\,-\,125\,)^{\,-\,\frac{2}{3}}\)

\(\displaystyle \L \;\,=\,\frac{1}{(\,-\,125)^{\frac{2}{3}}}\,\to\,\frac{1}{\sqrt[3]{15625}}\)

Use your calc to find the bottom value, the final answer is:\(\displaystyle \L \;\frac{1}{25}\)

 

[jwpaine]

I presume you mean (-125)^(-2/3) ?

forget the negative exponent for a sec

(-125)^(-2/3) = (-125^2)^(1/3) = 15625^(1/3) = ?

Thats a little high of a number to do a cubic root, with trial and error, isn't it? use your calc

x^3 = 15625 so x=25

so, because you have a negative exponent.. your answer is over 1

= 1/25

EDIT: Opps... sorry Jonboy!