How do you simplify and write #(a^4b^-3)/( ab^-2)# with positive exponents?

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Answer 1 · 2017-06-14T20:30:19

See a solution process below:

First, rewrite this expression as:

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

Use these rules for exponents to simplify the #a# terms:

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

#(a^4/a)(b^-3/b^-2) => (a^color(red)(4)/a^color(blue)(1))(b^-3/b^-2) => a^(color(red)(4)-color(blue)(1))(b^-3/b^-2) =>#

#a^3(b^-3/b^-2)#

Next, use these rules of exponents to simplify the #b# terms:

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

#a^3(b^color(red)(-3)/b^color(blue)(-2)) => a^3(1/b^(color(blue)(-2)-color(red)(-3))) => a^3(1/b^(color(blue)(-2)+color(red)(3))) =>#

#a^3(1/b^color(red)(1)) =>#

#a^3/b#