This is my first time writing, I hope this is the right forum for this. What does this mean?
"fraction numerator 48 over denominator square root of 16 to the power of begin display style 3 over 2 end style end exponent end root end fraction minus 3 to the power of 1 half end exponent times square root of fraction numerator 4 plus square root of 4 over denominator 2 end fraction end root"
On
This looks like a bad amalgamation of nested math formatting pseudocode with the escape characters removed. That, and the nesting is a bit loosy-goosy and ill-defined.
But, let's try anyway.
(By the way, real math isn't formatted like this. This is a mess. Did you pull this from a text version of a web page or something?)
I'll try to reformat the statement to highlight the structure.
fraction
numerator 48
over
denominator
square root of
16
to the power of
3 over 2
end exponent
end root
(end denominator)
end fraction
minus
3 to the power of
(start exponent)
1 half
end exponent
times
square root of
fraction
numerator
4 plus square root of 4
(end numerator)
over
denominator
2
(end denominator)
end fraction
end root
Taking this as the structure, the expression I put together looks like this:
$$\frac{48}{\sqrt{16^{3/2}}} - 3^{1/2}\times\sqrt{\frac{4+\sqrt{4}}{2}}$$
That's a bit hard to understand but this is what I think:
"fraction numerator 48 over denominator square root of 16 to the power of begin display style 3 over 2 end style end exponent end root end fraction" $\left(\frac{48}{\sqrt{16}}\right)^{3/2}= \left(\frac{48}{4}\right)^{3/2}= 12^{3/2}= (2\sqrt{3})^3= 24\sqrt{3}$
"minus 3 to the power of 1 half end exponent times square root of fraction numerator 4 plus square root of 4 over denominator 2 end fraction end root" Here I have a problem- the standard interpretation of this is that the exponent applies to the "3" but you might intend it to apply to the entire thing. Using the standard interpretation this will be $24\sqrt{3}- \sqrt{3}+ \sqrt{\frac{4}{2}}= 23\sqrt{3}+ \sqrt{2}$