How do you simplify #(2x^(-7/4))/(4x^(4/3))#?

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Answer 1 · 2016-12-19T14:42:12

#1/(2x^(37/12))#

We can modify this expression to:

#(2*x^(-7/4))/(2*2*x^(4/3)#

#(color(red)(cancel(color(black)(2)))*x^(-7/4))/(color(red)(cancel(color(black)(2)))*2*x^(4/3)#

#x^(-7/4)/(2x^(4/3))#

We can now use the rule for exponents which states:

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

#1/(2x^(4/3 - -7/4))#

#1/(2x^(4/3 + 7/4))#

#1/(2x^(16/12 + 21/12))#

#1/(2x^(37/12))#