## smartgirl101 3 years ago 3^5*3^2 9^4*9^5 7^4*7^2

1. phi

use the idea $b^{a}\cdot b^c = b^{a+c}$

2. phi

It comes down to adding up small integers.

3. phi

Do you follow?

4. smartgirl101

NO

5. phi

The formula is short hand. Match the b in the formula to the base in your question b^a * b^c 3^5 * 3^2 match the b to 3. match the a to 5. match c to 2 Can you do that. Now use this b^a * b^c = b^(a+c) answer is b to the (a+c) power. add up a and c to get the power

6. smartgirl101

O.K I GOT IT NOW

7. phi

Here is another way to do this. 3^5 is a short way to write 3*3*3*3*3 (three times itself 5 times) 3^2 is a short way to write 3*3 (three times itself twice) so 3^5 * 3^2 is the same as 3*3*3*3*3 * 3*3 count the number of 3's, and use the short way to write the answer 3^7

8. phi

Of course, it is faster to use the formula, because doing 3^20 * 3^10 means writing a lot of 3's. It's easier to just add 20+10 and get the answer 3^30

9. phi

Can you do 9^4*9^5 ?