Question 135675
4^-x=1/256


I would start be rewriting 1/256 as 256^-1.  You see, a number raised to a NEGATIVE exponent = the same number raised to a POSITIVE exponent UNDER 1.

So, 256^-1 = 1/256^1 = 1/256.

We now have:

4^-x = 256^-1

We now have to write 256 using a base 4.

Keep in mind that 4^4 = 256.

Then:

4^-x = 4^4

Do you see how we now have the SAME BASE 4 on both sides?

This was our goal.

Since we now have the same base on both sides, simply equate the exponents and solve for x.

-x = 4

x = 4/-1

x = -4

That's it!

Did you follow?