Is there any easy way to remember how to change them to a rational number or if you need to change them to a fraction? I find it difficult to remember all the rules and then when there is a difficult one I get confused as what to do first.
Thanks.
Is there any easy way to remember how to change them to a rational number or if you need to change them to a fraction? I find it difficult to remember all the rules and then when there is a difficult one I get confused as what to do first.
Thanks.
A rational number IS a number which can be expressed as a fraction. But this is how you do the things you are talking about:
to go from $\displaystyle \sqrt {4}$ to an indice is $\displaystyle 4^{\frac {1}{2}}$
if you are presented with a problem like $\displaystyle 64^{\frac {2}{3}}$ then all you do is cube root the number 64 and then square it, or the other way round. so you raise the number to the power of the number on the top (2 in this case) and then find nth root of that number where n is the number on the bottom of the fraction. so the answer is the cube root of 64 = 4, then square that and you have 16.
you can do the reverse so if you want to write the cube root of a number as an indice, you just write $\displaystyle x^\frac {1}{n}$ where n is the nth root of your number.
$\displaystyle 6^{-1}$ is the same as $\displaystyle \frac {1}{6^{1}}$ so all you do when there is a minus sign is square or cube or raise the number to the power as usual, then put a 1 over it. so $\displaystyle 2^{-3}$ is just $\displaystyle \frac {1}{2^{3}}$ which is $\displaystyle \frac {1}{8}$
these are all i can think of at the moment. if you need to know anything else just ask.