How do you simplify #4a^3b^2*3a^-4b^-3# and write it using only positive exponents?

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Answer 1 · 2017-01-14T18:55:59

See entire simplification process below:

First, we need to group like terms:

#4a^3b^2*3a^-4b^-3 ->#

#(4*3)(a^3*a^-4)(b^2*b^-3)#

Now we can use this rule of exponents to combine like terms:

#x^color(red)(a) * x^color(blue)(b) = x^(color(red)(a) +color(blue)(b))#

#(12)(a^(3 + -4))(b^(2 + -3))#

#12a^(3 - 4)b^(2 - 3)#

#12a^-1b^-1#

To eliminate the negative exponent we can use this rule for exponents:

#x^color(red)(a) = 1/x^color(red)(-a)#

#12/(a^(- -1)b^(- -1))#

#12/(a^1b^1)#

The final rule of exponents we will use to complete the simplification is:

#a^color(red)(1) = a#

#12/(ab)#