# Division Properties of Exponents

#### jramirez23

##### New member
I need help with the following problem:

t to the negative fourth power inside parenthesis to the ninth power
OVER
t to the negative fourth power inside parenthesis to the third power

I am confused on how to start the problem. What I first did was invert the Ts to make their exponents positive, and then I used Power of a Power and multiplied the exponents together to get t^36 over t^12. I think that this answer is most likely wrong however.

#### wjm11

##### Senior Member
t to the negative fourth power inside parenthesis to the ninth power
OVER
t to the negative fourth power inside parenthesis to the third power

I am confused on how to start the problem. What I first did was invert the Ts to make their exponents positive, and then I used Power of a Power and multiplied the exponents together to get t^36 over t^12. I think that this answer is most likely wrong however.
Hi, Jramirez,

Remember you said you "inverted." Make sure that's reflected in your answer.

Here's just one way to look at the problem:

[(t^-4)^9]/[(t^-4)^3]

= (t^-36)/(t^-12)

= t^[-36 – (-12)]

= t^[-36 + 12]

= t^-24 = 1/(t^24)

#### jramirez23

##### New member
Thank you for responding! This was what I got for my other answer. I quickly reviewed my notes from past problems and I see that you only have to invert exponents to get them to be positive when they are on the outside of the parenthesis. I also think that when you invert something inside parenthesis, (in this case, the negative four) it will never change.