Need help with negative rational exponents - will give medal!
1/6-3 = 1/1/63 = 1 ÷ 1/63 = 1 .(multiplied by) 63/1 = 216

Question

Need help with negative rational exponents - will give medal!
1/6-3 = 1/1/63 = 1 ÷ 1/63 = 1 .(multiplied by)  63/1 = 216  <--This is the example I was given.

I understand all of these steps except the last one... to me, 63/1 is 63, then multiplied by 1 is still 63...so how did it turn out to be 216?

tkhunny · Answer

You MUST get better notation.  Very VERY difficult to understand what you are doing.  

Use the carat to indicate exponentiation.
"six to the 3rd" can be 6^3
"six to the -3rd" can be 6^(-3)

$\dfrac{1}{6^{-3}} = \dfrac{1}{\dfrac{1}{6^{3}}}$

Okay, first, I would suggest you NEVER do this.  Save yourself a TON of trouble and possibility for error like this...

$\dfrac{1}{6^{-3}} = 6^{3}$ - - Done!
6^3 = 6*6*6 = 36*6 = 216

Another example:

$\dfrac{5^{-2}}{4^{-5}} = \dfrac{4^{5}}{5^{2}}$ -- Absolutely no need to mess around with those wonderfully- and unnecessarily-complicated fractions.

kobeni-chan · Answer

oh! that made it a lot simpler lol

triciaal · Answer

@tkhunny I am so glad someone could translate!!!