Answer
$ a.\quad$ We are multiplying two powers with the same base. One exponent is negative, and one is positive. The result has the same base and its exponent is the sum of exponents.
$ b.\quad$ Prediction: $9^{5}\displaystyle \cdot 9^{-7}=9^{5-7}=9^{-2}=\frac{1}{9^{2}}=\frac{1}{81}$
$c.\qquad x^{n}\cdot x^{-m}=x^{n-m}$
Work Step by Step
Given above.
