Math help, please and thank you?

Question

1. 6^5 /6^3

2.6^2/6^7

3. 6^4/6^-1

4. 6^-2
________
6^9

5. 6^-2
__________
6^-9

6. a^3 * a^-10

7.a^3/ a^-10

8. a^6
-----------
a^11

9. a^-7
-----------
a^4

10. a^-7
-----------
a^-4

11. a^15
------------
a^14

12. a^15
-------------
a^15

Answer 1

don't let the radicals scare you! this is just an easy way of dealing with numbers that have the same root, i.e., 6^5 is 7776 and 6^3 is 216 and 7776/216 is 36 or 6^2!
So you can treat radicals as a form of addition (when multiplying) or subtraction when dividing see: 6^ (5-3) =6^2!
2. 6 ^(2-7) = 6^ -5 or 1/6^5 ( a negative radical means it should "change places" if it is in the numerator it moves to the denominator and vice versa)
Look at 6. a^3 *a ^-10, since they are multiplied, add the radicals:
a^ (3 + -10) = a^-7 or once again it moves to the denominator: 1/a^7.
# 9 is trying to trick you, but since the numerator is negative it is a^(-7-4) = a^ -11 so it is all in the denominator!
Now it's your turn!