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!

Tutor: Can you help me: How do I simplify this expression using positive exponents? 
{{{(-2a^(-4)b^2c^(-7))}}}×{{{(3^(-2)a^(-2)b^(-5)c^9)}}} 

Put a 1 under each expression:

{{{ (-2a^(-4)b^2c^(-7))/1}}}×{{{(3^(-2)a^(-2)b^(-5)c^9)/1}}}

In the first expression,
Bring the {{{a^(-4)}}} from the top to the bottom as {{{a^4}}}
Bring the {{{c^(-7)}}} from the top to the bottom as {{{c^7}}}

In the second expression,
Bring the {{{3^(-2)}}} from the top to the bottom as {{{3^2}}}
Bring the {{{a^(-2)}}} from the top to the bottom as {{{a^2}}}
Bring the {{{b^(-5)}}} from the top to the bottom as {{{b^5}}}

Leave all the factors with positive exponents on top:

{{{(-2b^2)/(1*a^4c^7)}}}×{{{c^9/(1*3^2a^2b^5)}}}

Erase the 1's on the bottom of the fractions and
Change the {{{3^2}}} to {{{9}}}.


{{{(-2b^2)/(a^4c^7)}}}×{{{c^9/(9a^2b^5)}}}

Indicate the multiplication of the tops and the bottoms:

{{{(-2b^2c^9)/(a^4c^7*9a^2b^5)}}}

Add the exponents of {{{a^4}}} and {{{a^2}}} in the bottom
to get {{{a^6}}} and write the {{{9}}} factor first:


{{{(-2b^2c^9)/(9a^6c^7b^5)}}}

Now subtract the exponents of the b's, larger - smaller,
that is, 5-2=3 and place {{{b^3}}} on the bottom because the
larger exponent {{{b^5}}} was on the bottom:

{{{(-2c^9)/(9a^6c^7b^3)}}}
 
Finally subtract the exponents of the c's, larger - smaller,
that is, 9-7=2 and place {{{c^2}}} on the top because the
larger exponent {{{c^9}}} was on the top:

{{{(-2c^2)/(9a^6b^3)}}}

Edwin