SOLUTION: Question/Statement: "Suppose that the daily demand for milk shakes is given by q = 100p^-.5. To invert this demand function, you need to solve for p as a function of q. To get p on

Question 1045309: Question/Statement: "Suppose that the daily demand for milk shakes is given by q = 100p^-.5. To invert this demand function, you need to solve for p as a function of q. To get p on one side of q = 100p^-.5, you can first multiply both sides of this equation by p^.5. This yields qp^.5 = 100. Dividing both sides of this equation by q yields p^.5 = 100/q. Squaring both sides of this equation yields p = 10,000/q2. Thus, g(p) = 10,000/q2 is the inverse demand function."
My question: Can someone explain why in the first step, 100P^-.5 * p^.5 = 100? Do the exponents -.5 + .5 get added which from p^0, which is equal to 1?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the original equation is q = 100p^-.5

your question:

Can someone explain why in the first step, 100P^-.5 * p^.5 = 100? Do the exponents -.5 + .5 get added which from p^0, which is equal to 1?

my answer:

100 * p^(-.5) * p(5) = 1.

p^(-.5) = 1/p^5.

therefore p^(-.5) * p(5) = 1/p^5 * p^5 = p^5 / p^5 = 1.

100 * 1 = 100.

also, by the rules of exponent arithmetic, p^(-.5) * p^(.5) = p^(-.5 + .5) = p^(0) = 1.

there are basic rules of exponent arithmetic that need to be followed.

here's a tutorial that discusses them.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut26_exp.htm

here's another one.

http://www.purplemath.com/modules/exponent.htm

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