SOLUTION: Please help us to simplify the expression and leave anser with only positive exponents: {{{(p^(-3)+q^(-2))/q^(-1)}}}

Algebra ->  Exponents -> SOLUTION: Please help us to simplify the expression and leave anser with only positive exponents: {{{(p^(-3)+q^(-2))/q^(-1)}}}       Log On


   

Question 538688: Please help us to simplify the expression and leave anser with only
positive exponents: %28p%5E%28-3%29%2Bq%5E%28-2%29%29%2Fq%5E%28-1%29
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
%28p%5E%28-3%29%2Bq%5E%28-2%29%29%2Fq%5E%28-1%29
Make two fractions:

p%5E%28-3%29%2Fq%5E%28-1%29 + q%5E%28-2%29%2Fq%5E%28-1%29

Get all the negative exponents positive by

using this rule: X%5E%28-N%29%2FY%5E%28-M%29 = Y%5EM%2FX%5EN

[That is, an exponential with a negative exponent 
which is a numerator (denominator) or a factor 
thereof may be brought from the numerator(denominator) 
to the denominator (numerator), and the sign of the
exponent changed to positive.]

q%5E1%2Fp%5E3 + q%5E1%2Fq%5E2
  
In the second fraction, we can divide top and bottom by q:

q%5E1%2Fp%5E3 + 1%2Fq%5E1

We can erase the 1 exponents

q%2Fp%5E3 + 1%2Fq

That is one form of the answer.  Or you can combine the
fractions over the LCD of p³q

%28q%5E2%2Bp%5E3%29%2F%28p%5E3q%29

Edwin