SOLUTION: The expression: x^2 (1/9x^3) (63x^-11) equals c/x^e where the coefficient c is ___? and the exponent e is ___ ?

Algebra ->  Exponents -> SOLUTION: The expression: x^2 (1/9x^3) (63x^-11) equals c/x^e where the coefficient c is ___? and the exponent e is ___ ?      Log On


   

Question 392998: The expression: x^2 (1/9x^3) (63x^-11) equals c/x^e where the coefficient c is ___? and the exponent e is ___ ?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2A%281%2F9x%5E3%29%2A%2863x%5E%28-11%29%29
First we will simplify the expression. Then we will put it in the c%2Fx%5Ee form.

To multiply we will start by making everything a fraction:
%28x%5E2%2F1%29%2A%281%2F9x%5E3%29%2A%2863x%5E%28-11%29%2F1%29
When we multiply the numerators we will use the rule for exponents when we multiply the x's: Add the exponents:
%2863x%5E%282%2B%28-11%29%29%29%2F%289x%5E3%29
which simplifies to:
%2863x%5E%28-9%29%29%2F%289x%5E3%29
63/9 = 7 and to divide the x's we use the rule for exponents when you divde: Subtract the exponents:
7%2Ax%5E%28-9-3%29
or
7%2Ax%5E%28-12%29
The expression is now simplified. To put it in c%2Fx%5Ee form we will use a property of negative exponents: a%5E%28-q%29+=+1%2Fa%5Eq
7%2A%281%2Fx%5E12%29
which simplifies to
7%2Fx%5E12
We can now see that c = 7 and e = 12.