How do you write ##1/169## as a negative exponent?

##169^-1## or ##13^-2##
When working with exponents a negative exponent always results in a fraction, be it ##2^-2## or ##3^-123##. This is simply because a rule of exponents to keep exponents positive.
Example:
##2^-5=1/2^5##
In your case to write ##1/169## as a negative exponent isn’t complicated. You would simply add a negative exponent sign to the denominator. However knowing that ##169## is a perfect square you can write your answer two ways; simply moving the denominator to the top: ##169^-1## or simplifying all the way: ##13^-2##, I believe your teacher would likely prefer the more simplified version.
TL;DR
negative exponent = fraction
remove fraction, add neg exponent, simplify