SOLUTION: Write each of the following expressions as a single power of x. a) x^-6*x^5 b) x^3/x^-6 c) (x^-6)^5

Algebra ->  Exponents -> SOLUTION: Write each of the following expressions as a single power of x. a) x^-6*x^5 b) x^3/x^-6 c) (x^-6)^5      Log On


   

Question 282224: Write each of the following expressions as a single power of x.
a) x^-6*x^5
b) x^3/x^-6
c) (x^-6)^5
Found 2 solutions by jim_thompson5910, Mathematicians:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a) Use the identity x%5E%28y%29%2Ax%5E%28z%29=x%5E%28y%2Bz%29. In other words, simply add the exponents (when you multiply monomials)

b) Use the identity %28x%5E%28y%29%29%2F%28x%5E%28z%29%29=x%5E%28y-z%29 (now we're subtracting exponents).

c) Now we're multiplying exponents. So use the identity %28x%5E%28y%29%29%5Ez=x%5E%28y%2Az%29

Answer by Mathematicians(84) About Me  (Show Source):
You can put this solution on YOUR website!
a) x%5E-6%2Ax%5E5
b) x%5E3%2Fx%5E-6
c) %28x%5E-6%29%5E5
x%5E-6%2Ax%5E5
add the exponents together:
-6+%2B+5+=+-1
x%5E-1
x%5E3%2Fx%5E-6
subtract the second from the first:
3+-+%28-6%29=+9
x%5E9
%28x%5E-6%29%5E5
multiply the exponents:
-6+%2A+5+=+-30
x%5E-30