Melody

$${\sqrt{{\mathtt{640}}}} = {\mathtt{25.298\: \!221\: \!281\: \!347\: \!034\: \!7}}$$    that is an approximation

or

$$\sqt{640}=8\sqrt{10}$$

you can do the other one.   

thanks anon,

of course you are correct. 

It is funny, I missed that.  

The reason I missed it is that my mind went back to to computer programming days.

when

x=x^24

would have meant REPLACE x with the old value of x raised to the power of 24.

that link doesn't work Nauseated

Is this a touch of CDD I see here Alan?  There seems to be an epidemic a presen.   (woops, no t)

My computer is refusing to type t's half the time.  I think that it has CDD too!     

Now Bertie it is your responsibility to find us a new riddle!     LOL

I did this a moment ago.  Do not fill the board with repeat questions.  Thank you.

If you need to repost - here are the instructions.

Please follow them as it makes the forum better for everyone.

$$\\\frac{12^x}{48^{2x}}\\\\
=\frac{12^x}{(12*4)^{2x}}\\\\
=\frac{12^x}{12^{2x}*4^{2x}}\\\\
=\frac{1}{12^x*4^{2x}}\\\\
=\frac{1}{3^x*4^{x}*4^{2x}}\\\\
=\frac{1}{3^x*4^{3x}}\\\\
=\frac{1}{3^x*64^x}}\\\\
=\frac{1}{192^x}}\\\\$$

Maybe I have CDD           I have probably done this the long way and there might be errors.  

Mmm

Lets see.

$$\\\dfrac{4\times 2^{1/4}\times8^{1/6}}{16^{3/4}}\\\\\\
=\dfrac{2^2\times 2^{1/4}\times(2^3)^{1/6}}{(2^4)^{3/4}}\\\\\\
=\dfrac{2^2\times 2^{1/4}\times 2^{3/6}}{2^{12/4}}\\\\\\
=\dfrac{2^2\times 2^{0.25}\times 2^{0.5}}{2^{3}}\\\\
=2^{2+0.25+0.5-3}\\\\
=2^{-0.25}\\\\
=\frac{1}{2^{1/4}}\\\\
=\frac{1}{\sqrt[4]{2}}$$

$$\\\frac{12^x}{6^x\times8^x}\\\\
=\frac{6^x\times 2^x}{6^x\times2^x\times 4^x}\\\\
=\frac{1}{ 4^x}\\\\$$

example

$$\\6\frac{3}{8}-2\frac{2}{8}\\\\
=6+\frac{3}{8}-2-\frac{2}{8}\\\\
=6-2+\frac{3}{8}-\frac{2}{8}\\\\
=4+\frac{1}{8}\\\\
=4\frac{1}{8}$$