How do you calculate 10 to the power of -2.8?

Answer 1

12.8

Answer 2

This is best done on a scientific calculator - the details of the calculation are just too involved to regularly do it by hand.

Such a power can be defined in terms of logarithms and antilogarithms:

x = 102.8

ln x = ln 102.8

ln x = 2.8 ln 10

Now, take antilogs on both sides:

x = exp(2.8 ln 10)

In general, ab (for positive a and b) is equal to exp(b ln a).

exp is the exponential function, ln is the natural logarithm. Both can be calculated as infinite sums, as shown in calculus courses. For example:

exp x (same as ex) is equal to 1 + x + x2/2! + x3/3! + x4/4! + ...

The idea that after adding some terms, you get close enough to the final result, so you don't really have to add an infinite number of terms. (The individual terms eventually get smaller and smaller.)

How about this:

10^-2.8 you probably do the same as above but take a reciprocal to then find the answer since:

10^-2.8 = 1/10^2.8