Hi everyone,

I was going through some example questions in preparation for my test, and came across this one:

It seems simple enough, but I’m having so much trouble evaluating the first option:

(1/2)^{(1/6)}

I am familiar with most exponent rules, but I’m stuck on trying to get the value of the first option without running into cube roots — which are outside of my comfort zone. Anyone have a better way?

Thanks for the help.

-Joe

Reason its value out.

\left(\frac{1}{2}\right)^{\frac{1}{6}} = \frac{1}{2^\frac{1}{6}}

Now, 2^\frac{1}{6} is somewhere between 2^{0} (which is 1) and 2^{1} (which is 2). In other words, 1 < 2^\frac{1}{6} < 2. Hence we can show that

\frac{1}{2} < \frac{1}{2^\frac{1}{6}} < 1

That is, there is no need to evaluate the cube root, rather we are using reasoning to show that it must be within a certain range.

1 Like

Brilliant.

Thank you for the response – this makes good sense.

-Joe