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 20 (which is 1) and 21 (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.
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Brilliant.
Thank you for the response – this makes good sense.
-Joe