How do you simplify #2^(5/2) - 2^(3/2)#?

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Answer 1 · 2015-04-09T11:39:30

In general
#b^(p+q) = b^p*b^q#
so
#2^(5/2)# can be re-written as #2^(3/2)*2^(2/2) = 2^(3/2)*2#

#2^(5/2)-2^(3/2)#

#= 2^(3/2)(2-1)#

and since
#2^(3/2) = (2^3)^(1/2) = 2sqrt(2)#

#2^(5/2)-2^(3/2) = 2sqrt(2)#

Answer 2 · 2017-07-17T07:02:52

#2sqrt2#

Do not be tempted to simplify the indices. These are separate terms.

However, we can factorise and take out a common factor of #2^(3/2)#.

When you are dividing and the bases are the same, subtract the indices.

#2^(5/2) -2^(3/2) = 2^(3/2)(2^(2/2) -1)#

#=2^(3/2)(2-1) = 2^(3/2)(1)#

#2^(3/2)# can also be written as: #" "2^(2/2+1/2) = 2xx2^(1/2)#

#=2sqrt2#

Another approach to simplify this is:

#2^(3/2) = sqrt(2^3) = sqrt 8 = sqrt(4xx2)#

#=2sqrt2#