[{(3 to power 5by2*5 to power 3by4)/2to power -5by4}/{16/5 to power 1by4*3 to power 1by2)}]to power 1by5

Answer 1

I cannot interpret all those words. What is "by" supposed to mean?

Is 3 to power 5by2

2*3^5 or (3^5)^2

That is, does by mean multiply by or raise to a new power?

Try using
* for multiply
^ for exponent
() to make it clear what is grouped

Ahhh. I think the "by" means division, right? So why not just use / everywhere? I think you have

[{(3^(5/2) * 5^(3/4)) / 2^(-5/4)}/{(16/5)^(1/4) * 3^(1/2)}]^(1/5)

Take a look at how wolframalpha interprets my version of your input. If I got it wrong, play around with the syntax till the displayed version matches what you want.

http://www.wolframalpha.com/input/?i=[{%283^%285%2F2%29+*+5^%283%2F4%29%29+%2F+2^%28-5%2F4%29}%2F{%2816%2F5%29^%281%2F4%29+*+3^%281%2F2%29}]^%281%2F5%29