How do you simplify #\frac { 3u v ^ { - 4} } { 2u ^ { - 1} }#?

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Answer 1 · 2017-04-12T21:23:48

See the entire solution process below:

First, use this rule of exponents to rewrite the numerator:

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

#(3u^color(red)(1)v^-4)/(2u^-1)#

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

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

#(3u^color(red)(1)v^-4)/(2u^color(blue)(-1)) = (3u^(color(red)(1)-color(blue)(-1))v^-4)/2= (3u^(color(red)(1)+color(blue)(1))v^-4)/2 = (3u^2v^-4)/2#

Now, use this rule of exponents to eliminate the negative exponent:

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

#(3u^2v^color(red)(-4))/2 = (3u^2)/(2v^color(red)(- -4)) = (3u^2)/(2v^color(red)(4))#