Simplifying Exponential Expressions: x^b/x or x^(b-1)?

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The discussion centers on simplifying the expression x^b/x. Participants argue that x^(b-1) is the simpler form, as it eliminates the division present in the original expression. The consensus leans towards x^(b-1) being more straightforward due to its cleaner representation. The conversation highlights the importance of clarity in mathematical expressions. Ultimately, x^(b-1) is favored for its simplicity.
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Homework Statement



I was told to simplify and don't know which one is more "simple"

x^b/x or x^(b-1)?

Homework Equations





The Attempt at a Solution

 
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GreenPrint said:

Homework Statement



I was told to simplify and don't know which one is more "simple"

x^b/x or x^(b-1)?

Homework Equations





The Attempt at a Solution

IMO, xb - 1 is the simpler of the two expressions. In the other expression, there is an obvious division that could be performed.
 
thanks
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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