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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 = z^{9 - 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 = t^{12 - 36} = t^{- 24}

I hope this helps,
Harley

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