SOLUTION: Tutor: Can you help me: How do I simplify this expression using positive exponents? (-2a^-4b^2c^-7) (3^-2a^-2b^-5c^9) I started by -2*9 a^-6b^-3c^2 -18c^2/a^6b^3 bu

Algebra ->  Exponents -> SOLUTION: Tutor: Can you help me: How do I simplify this expression using positive exponents? (-2a^-4b^2c^-7) (3^-2a^-2b^-5c^9) I started by -2*9 a^-6b^-3c^2 -18c^2/a^6b^3 bu      Log On


   

Question 84755: Tutor: Can you help me: How do I simplify this expression using positive exponents?
(-2a^-4b^2c^-7) (3^-2a^-2b^-5c^9)
I started by -2*9 a^-6b^-3c^2 -18c^2/a^6b^3
but I got confused about dividing!
Thank you!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Tutor: Can you help me: How do I simplify this expression using positive exponents?
(-2a^-4b^2c^-7) (3^-2a^-2b^-5c^9)
I started by -2*9 a^-6b^-3c^2 -18c^2/a^6b^3
but I got confused about dividing!
Thank you!
Tutor: Can you help me: How do I simplify this expression using positive exponents?
%28-2a%5E%28-4%29b%5E2c%5E%28-7%29%29×%283%5E%28-2%29a%5E%28-2%29b%5E%28-5%29c%5E9%29
Put a 1 under each expression:
+%28-2a%5E%28-4%29b%5E2c%5E%28-7%29%29%2F1×%283%5E%28-2%29a%5E%28-2%29b%5E%28-5%29c%5E9%29%2F1
In the first expression,
Bring the a%5E%28-4%29 from the top to the bottom as a%5E4
Bring the c%5E%28-7%29 from the top to the bottom as c%5E7
In the second expression,
Bring the 3%5E%28-2%29 from the top to the bottom as 3%5E2
Bring the a%5E%28-2%29 from the top to the bottom as a%5E2
Bring the b%5E%28-5%29 from the top to the bottom as b%5E5
Leave all the factors with positive exponents on top:
%28-2b%5E2%29%2F%281%2Aa%5E4c%5E7%29×c%5E9%2F%281%2A3%5E2a%5E2b%5E5%29
Erase the 1's on the bottom of the fractions and
Change the 3%5E2 to 9.

%28-2b%5E2%29%2F%28a%5E4c%5E7%29×c%5E9%2F%289a%5E2b%5E5%29
Indicate the multiplication of the tops and the bottoms:
%28-2b%5E2c%5E9%29%2F%28a%5E4c%5E7%2A9a%5E2b%5E5%29
Add the exponents of a%5E4 and a%5E2 in the bottom
to get a%5E6 and write the 9 factor first:

%28-2b%5E2c%5E9%29%2F%289a%5E6c%5E7b%5E5%29
Now subtract the exponents of the b's, larger - smaller,
that is, 5-2=3 and place b%5E3 on the bottom because the
larger exponent b%5E5 was on the bottom:
%28-2c%5E9%29%2F%289a%5E6c%5E7b%5E3%29

Finally subtract the exponents of the c's, larger - smaller,
that is, 9-7=2 and place c%5E2 on the top because the
larger exponent c%5E9 was on the top:
%28-2c%5E2%29%2F%289a%5E6b%5E3%29
Edwin