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)*

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.