How do you evaluate #\frac { b ^ { \frac { 2} { 2} } } { 4b ^ { 2} } - \frac { 2b ^ { - 3} } { 4b ^ { 2} }#?

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Answer 1 · 2017-12-16T06:57:47

#=\frac{b^4-2}{4b^5}#

#\frac { b ^ { \frac { 2} { 2} } } { 4b ^ { 2} } - \frac { 2b ^ { - 3} } { 4b ^ { 2} }#

#= \frac { b ^ 1 } { 4b ^ { 2} } - \frac { 2b ^ { - 3} } { 4b ^ { 2} }#

As the denominators are equal,

#= frac { b ^ 1 - 2b^-3 } { 4b ^ { 2} } #

#= frac {b (1 - 2b^-4) } { 4b ^ { 2} } #

#= frac {cancelb (1 - 2b^-4) } { 4b ^ { cancel2} } #

#= frac {1 - 2b^-4 } { 4b } #

Rule #a^-m =1/a^m#

#= frac {1 - 2(1/b^4) } { 4b ^ { 1} } #

Make denominators of the numerator fraction equal :

#= frac {1(b^4/b^4) - 2(1/b^4) } { 4b ^ { 1} } #

#= frac {(b^4 -2))(b^4)/ { 4b ^ 1} #

#= (b^4 -2)/(b^4) xx 1/ { 4b ^ 1} #

Rule: #a^m xx a^n = a^(m+n)#

#= (b^4 - 2)/ (4 b^5)#