   SEARCH HOME Math Central Quandaries & Queries  Question from Bill, a student: 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 did was invert the Ts to make them positive and I then multiplied the powers. I am not sure if this is the correct process. Hi Bill,

There are different ways to approach this problem. One way is to see t- 4 as one symbol, let me say z = t- 4, and then see

(t- 4)9/(t- 4)3 as z9/z3 = z9 - 3 = z6 = (t- 4)6 = t- 24

In fact if you see t- 4 as one symbol you don't need the z at all.

(t- 4)9/(t- 4)3 = (t- 4)9 - 3 = (t- 4)6 = t- 24

You could however proceed the way you suggest. write t- 4 as 1/t4 and get

(t- 4)9/(t- 4)3 = (1/t4)9/(1/t4)3 = 1/t36 × t12/1 = t12 - 36 = t- 24

I hope this helps,
Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.