I have troubles with any difference of squares expression that incorporates a fraction.
For instance in the expression
=
I understand the here comes from , however I have no clue how we get from . Would someone please enlighten me?
Thank you
For this problem you have to know that
We do not use the cube because we're taking the square root of the entire which means both the 1/64 and the x^6 should be raised to the power of 1/2.
Imagine that the 64 is raised to the power of 1. Like you did with the x^6 we can divide the exponent by 2 to give 64^(1/2) = 8
Interestingly (although off topic) this expression is also the difference of two cubes
Thanks guys, what I have been doing is just taking the number or fraction and raising it to ^(1/2) and it has worked for every problem except this one, so I guess this trick doesnt always work.
For instance
Taking unfortunately does not yield either of the simplified fractions listed above, rather
Edit Update: Well I guess I take that back. For some reason in my TI-83 if I just enter it will yield
but if I do , turn it back into the fraction and then raise that to it will give me the correct fraction
Very strange indeed, anyone know why the calculator might be doing this?
Sounds like you didn't use parentheses when you inputted into the calculator, as cmf0106 suggests. You really have to be careful about things like that. If you typed something like
16/81^(1/2)
then only the 81 is going to be raised to the 1/2 power because of order of operations. If you want to raise the entire fraction to the 1/2 power you need parentheses:
(16/81)^(1/2)
01