Answer:
The Index notation for 3x7x7x7x7 is:
![3* 7^4](https://img.qammunity.org/2019/formulas/mathematics/high-school/7t6nd0z3mn8ucgryohu8a2td6ordcsmied.png)
The Index notation for 2x9x9x9x2x9 is:
![2^2* 9^4](https://img.qammunity.org/2019/formulas/mathematics/high-school/qlfli07swy3jw6eg87a1nflnat0uxz2vq0.png)
Explanation:
Consider the provided number.
3×7×7×7×7 and 2×9×9×9×2×9
We need to write the number in index notation.
Index notation is shortcut method of writing repeated multiplications by the same number.
Consider the number.
![3* 7* 7* 7* 7](https://img.qammunity.org/2019/formulas/mathematics/high-school/qj8u67h80ht43yqj0eeendvz1n87u65b6s.png)
Here, 3 repeat 1 time and 7 repeat 4 times.
Thus, the Index notation is:
![3* 7* 7* 7* 7=3* 7^4](https://img.qammunity.org/2019/formulas/mathematics/high-school/874b6xe2ztky59ouawy65adot1futg9jdg.png)
Consider the second number.
![2* 9* 9* 9* 2* 9](https://img.qammunity.org/2019/formulas/mathematics/high-school/5xd46x1nr8xank6ajlyree5vdahj0gyuty.png)
Here, 2 repeat 2 times and 9 repeat 4 times.
Thus, the Index notation is:
![2* 9* 9* 9* 2* 9=2^2* 9^4](https://img.qammunity.org/2019/formulas/mathematics/high-school/2bexmgi6hy40dywlo2bemg0lom7rxd2pcs.png)