Find the quotient

$${\frac{{{\mathtt{10}}}^{{\mathtt{6}}}}{{{\mathtt{10}}}^{{\mathtt{7}}}}}$$

also, if you just think about it for a moment.  You have got 6 tens on the top and 7 tens on the bottom when you cancel you will be left with just 1 ten and it will be on the bottom.  The top cancels out to 1

$$\frac{10^6}{10^7}=\frac{10*10*10*10*10*10}{10*10*10*10*10*10*10}=\frac{1}{10}$$

Also as CPhill said

$$\frac{10^6}{10^7} = 10^{6-7}=10^{-1}$$

therefore

$$10^{-1}=\frac{1}{10}$$

Look here for more info on indices - especially negative indices.

http://web2.0calc.com/questions/indices-especially-negative-indices

Remember the rule of exponents here......  aⁿ / a^m   =   a^n-m

So ...if I had......  5⁶/5²   ...it would equal........  5^6-2  =  5⁴

Now...see if you can do yours, based on this....if not.....let me know.....