How do you multiply #(\frac { u ^ { 3} v ^ { - 1} } { 2w ^ { 3} } ) ^ { - 3} ( v w ^ { 3} )#?

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Answer 1 · 2016-11-30T17:36:33

#(8v^4w^27)/u^9#

Dealing with the first pair of brackets first

#((u^3v^(-1))/(2w^3))^(-3) " is the same as "((2w^3)/(u^3v^(-1)))^3#

The #v^(-1)" is the same as "1/v " so "1/v^(-1) = v#

Thus the first bracket is:#" "((2vw^3)/(u^3))^3#

Cubing the contents of these bracket

#(8v^3w^9)/(u^9)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all together we have:

#(8v^3w^9)/(u^9)xxvw^3#

#=(8v^4w^27)/u^9#