How do you multiply #u^ { - \frac { 5} { 4} } v ^ { 2} \cdot ( u ^ { \frac { 3} { 2} } ) ^ { - \frac { 3} { 2} }#?

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Answer 1 · 2016-11-17T22:03:27

#v^2/u^(7/2) =v^2/(sqrtu)^7#

There are several laws of indices being applied here.

#u^(-5/4) v^2 xx (u^(3/2))^(-3/2)#

Remove the brackets #rarr# multiply the indices:

#u^(-5/4) v^2 xx u^(-9/4)#

When multiplying: add the indices of like bases:

=#u^(-5/4 -9/4) xx v^2#

=#u^(-14/4) xx v^2" "larr -14/4 = -7/2#

Change the negative index to a positive:

#v^2/u^(7/2)#

This can also be given as #v^2/(sqrtu)^7#