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Explanation of a simple exponent rule in a derivative problem needed

  • Thread starter AwesomeSN
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  • #1
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Explanation of a "simple" exponent rule in a derivative problem needed

After differentiation, I get this : 9(t-2/2t+1)8 * 5/(2t+1)2

Now this simplifies into 45(t-2)/(2t+1)10

Now, I am wondering what the property is that combines the exponent from the top with the bottom to get an power of 10 in the simplified form.

*Note. the t-2/2t+1 is t-2 over 2t+1, the 5/(2t+1)2 is 5 over (2t+1)2, and the 45(t-2)/(2t+1)10 is 45(t-2) over (2t+1)10.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
302
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From the rules of exponents:

[itex]a^n a^m = a^{n+m}[/itex]
 
  • #3
768
4


if you start with [tex] 9 (\frac{t-2}{2t+1})^8 * \frac{5}{(2t+1)^2} [/tex]
then you can write [tex] 9 \frac{(t-2)^8}{(2t+1)^8}* \frac{5}{(2t+1)^2} [/tex]
and then you add the exponents when multiplying like bases, thus getting [tex] 45 \frac{(t-2)^8}{(2t+1)^{10}} [/tex]

Note that [tex] (2t+1)^8(2t+1)^2=(2t+1)^{10} [/tex]

edit:
boo, pibond beat me cause I'm slow at latex! :P
 
Last edited:
  • #4
14
0


Thank you. I was aware of the rule for exponents, but applying the power of 8 to both the numerator and denominator escaped me, now it all makes sense!
 

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