How do you use the laws of exponents to simplify the expression #(-14a^2b^3)/ (5ab^10)#?

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Answer 1 · 2018-03-30T12:50:48

See a solution process below:

First, rewrite the expression as:

#-14/5(a^2/a)(b^3/b^10)#

Next, 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))# and #a^color(red)(1) = a#

#-14/5(a^2/a)(b^3/b^10) =>#

#-14/5(a^color(red)(2)/a^color(blue)(1))(b^3/b^10) =>#

#-14/5(a^(color(red)(2)-color(blue)(1)))(b^3/b^10) =>#

#-14/5(a^(color(red)(1)))(b^3/b^10) =>#

#-14/5(a)(b^3/b^10) =>#

#-(14a)/5(b^3/b^10)#

Now, use this rule of exponents to simplify the #b# term:

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

#-(14a)/5(b^color(red)(3)/b^color(blue)(10)) =>#

#-(14a)/5(1/b^(color(blue)(10)-color(red)(3))) =>#

#-(14a)/5(1/b^7) =>#

#-(14a)/(5b^7)#

Answer 2 · 2018-03-30T13:26:43

#(-14a)/(5b^7)#

#(-14a^2b^3)/(5ab^10)#

#:.=(-14a^(2-1))/(5b^(10-3))#

#:.=(-14a)/(5b^7)#