SOLUTION: Multiply and express the product in the simplest form. (x - 3)^3/2^3 * 1^2/(x-3)^2 Could someone explain how I should solve that problem?

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Multiply and express the product in the simplest form. (x - 3)^3/2^3 * 1^2/(x-3)^2 Could someone explain how I should solve that problem?      Log On


   

Question 144500: Multiply and express the product in the simplest form.

(x - 3)^3/2^3 * 1^2/(x-3)^2
Could someone explain how I should solve that problem?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given: %28%28x+-+3%29%5E3%2F2%5E3%29+%2A+%281%5E2%2F%28x-3%29%5E2%29+
Multiplying alegbraic fractions uses the same 'rules' as multiplication of plain old regualr fractions.
You make a simple product of the values in the numerator. Then do the same for the products of the terms in the denominator.
Then simply (cancel out) as best you can.
Finally multiply (expand) as makes sense.
In this case:
%28%28x+-+3%29%5E3%2F2%5E3%29+%2A+%281%5E2%2F%28x-3%29%5E2%29+
Multiply the two numerators and the two denominators, keeping their products "on their side of the division sign'.
%28%28x+-+3%29%5E3%2A+%281%5E2%29%29%2F%282%5E3+%2A+%28x-3%29%5E2%29+
You can see the term x-3 in both the numerator and the denominator. You can cancel out two of those as follows
%28%28x+-+3%29+%2A+%281%5E2%29%29%2F2%5E3+
Now finish your simplification by finding the values for the integer powers
%28%28x+-+3%29+%2A+1%29%2F8+
Lucky you, in this case, there is nothing left to expand since the 1 can be 'canceled'
%28x+-+3%29+%2F8+