Hello!
Using the property of exponents, when exponents are multiplied together, the powers are added together.
Here is basic format:
.
With that, add each exponent power together and simplify.
A).
![7^(-1) * 7^(-1) = 7^(-2) = (1)/(49)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/lrkoe4c3aqfg7shmkxsfcdkyw9pevfxo16.png)
B).
![7^(8) * 7^(-6) = 7^(2) = 49](https://img.qammunity.org/2019/formulas/mathematics/middle-school/g8vx2ybtrfe10ug4v5vt3cep0pjfl3mckr.png)
C).
![7^(-5) * 7^(3) = 7^(-2) = (1)/(49)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/oshcw1w6msz1x07qgbfnum0sud3ghyxw0e.png)
D).
![7^(7) * 7^(-9) = 7^(-2) = (1)/(49)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/2rh4gcegwta9f38l6jpnsgpbghkfc0ryul.png)
E).
![7^(-2) * 7^(4) = 7^(2) = 49](https://img.qammunity.org/2019/formulas/mathematics/middle-school/14hdk0ecrh56vx0nwpa7acu6vvkm40d6w0.png)
Therefore, the expressions equivalent to 1/49 are A, C, and D.