7^-1+9^-1, how do you solve this exponent equation?

Raising to a negative power just makes the base value into a fraction

For example, x^-1 turns into (1/x^1)

This means that your equation goes from
7^-1+9^-1 to (1/7)+(1/9)

1/7+1/9 simplifies to 16/63 after all of the common denominator stuff

So, in short 7^-1+9^-1 = 16/63