Given that, in standard form, 3^236 is approx. 4 * 10 ^ 112 and 3^(-376) is approx. 4 * 10^(-180), find the approximation in standard form for 3^376.

Hello!
To answer this question we only need the fact  3^(-376) approx 4*10^(-180).
By the definition, raise some number b to a negative natural power -n means 1) raise b to the positive power n and 2) divide 1 by the result. This is the formula:
b^(-n) = 1/(b^n).
As you can easily infer from this formula,
b^(n) = 1/(b^(-n))                                                     (1)
is also true.
In our task, n = 376 and b = 3. So we have
3^376 = 1/(3^(-376)).
The number at the denominator is approximately known, so
3^376 = 1/(3^(-376)) approx 1/(4*10^(-180)) = 1/4*1/(10^(-180)) = 0.25*1/(10^(-180)).
Now we use the formula (1) in the reverse direction for b = 10 and n = 180:
1/10^(-180) = 10^180.
This way the number in question is about
0.25*10^180 = 0.25*10*10^179 = 2.5*10^179  
(standard form requires factor between 1 and 10 ).
So the answer is:  3^376 approx 2.5*10^179.
(if you actually need 3 in some other degree, please reply and I'll try to help)