How do you simplify #9^(3/2)#?

Question

114617 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-25T09:18:39

#27#

Breaking #9^(3/2)# down into its component parts

#3/2# is the same as #3xx1/2# which is the same as #1/2xx3#

so #9^(3/2)# is the same as #9^(1/2xx3)#

Write this as: #(9^(1/2))^3#

Consider the part of #9^(1/2)#

This is the same as #sqrt(9) = 3#

So #(9^(1/2))^3 = (sqrt(9))^3#

#=3^3=27#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
However, it true to say that:

#sqrt(9)=+-3#

and #(+-3)^3=+-27#