How do you simplify the expression #(8e^-4f^-2)/(18ef^-5)# using the properties?

1 Answer
Jun 7, 2017

Answer:

See a solution process below:

Explanation:

first, simplify the constants as:

#(8e^-4f^-2)/(18ef^-5) = ((2 xx 4)e^-4f^-2)/((2 xx 9)ef^-5) =#

#((color(red)(cancel(color(black)(2))) xx 4)e^-4f^-2)/((color(red)(cancel(color(black)(2))) xx 9)ef^-5) = (4e^-4f^-2)/(9ef^-5)#

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

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

#(4e^-4f^-2)/(9ef^-5) = (4e^color(red)(-4)f^-2)/(9e^color(red)(1)f^-5) = #

#(4f^-2)/(9e^(color(red)(1)-color(red)(-4))f^-5) = (4f^-2)/(9e^(color(red)(1)+color(red)(4))f^-5) =#

#(4f^-2)/(9e^5f^-5)#

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

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

#(4f^color(red)(-2))/(9e^5f^color(blue)(-5)) = (4f^(color(red)(-2)-color(blue)(-5)))/(9e^5) =#

#(4f^(color(red)(-2)+color(blue)(5)))/(9e^5) = (4f^3)/(9e^5)#