1]
Subtract
SOLUTION
a ) The first step is to factor the denominators.
b ) The second step is to write down the LCD of the fractions.
LCD =
c ) The third step is to write the two fractions as equivalent fractions
with the LCD as their common denominator.
d ) The fourth step is to combine - subtract, in this example - the two fractions.
e ) The fifth step is to reduce the resulting fraction in step 4)
to lowest terms in order to get the final answer.
Cancel the common factor
that appears in the numerator and denominator of the fraction.
2]
Write
with
positive exponents only.Use the definition of negative exponents as reciprocals to do this.
SOLUTION
Now we can use the rule for dividing fractions, just like in arithmetic,
invert the divisor and multiply.
We can express this result as kind of rule,
when you have a fraction of exactly the form given above:
The negative exponent on the top (the numerator) goes down to the bottom (the denominator)
and becomes positive.
The negative exponent on the bottom (the denominator) goes up to the top (the numerator)
and becomes positive.
3]
All the properties of exponents - given in Theorem 1 on page 44 , for integer exponents -
work no matter what the exponents are.
Positive or negative integers, rational or irrational numbers.
Simplify
.SOLUTION
We use the rules for the order of operations, do the stuff inside the parentheses first.
When we raise a product to a power, raise each factor of the product to that power.
or 
top
© edmond 2003