How can you write 1/256 using a negative exponent other than -1?
To express 1/256 using a negative exponent other than -1, we can start by rewriting 1/256 as 256 raised to a negative exponent.
We know that any number raised to the power of -n is equal to 1 divided by that number raised to the power of n. So, to find the negative exponent other than -1 that represents 1/256, we can express it as:
1/256 = 256^(-n)
Now, to determine the value of the negative exponent, we need to equate the two expressions:
256^(-n) = 1/256
To solve for n, we can use logarithms. Taking the logarithm base 256 of both sides, we have:
log(base 256) (256^(-n)) = log(base 256)(1/256)
Next, we can apply the power rule of logarithms, which states that log(base a) (a^b) = b. Using this rule, we get:
(-n) = -1
Finally, solving for n, we get:
n = 1
Therefore, 1/256 can be written using a negative exponent other than -1 as 256^(-1).