Question

2^(5/2)-2^(3/2)
Why is the answer to this equation 2^(3/2)

Answer 1

think of how \(2^{5/2}\) can be rearranged

Answer 2

\[2^{5/2}=2^{(3+2)/2}=2^{3/2+2/2}=2^{3/2+1}=2\times2^{3/2}\]

Answer 3

@GluttonousIntention09 this is why:
\[2^{2.5} - 2^{1.5}\]
\[= 2^{(2+0.5)} - 2^{(1+0.5)}\]
=\[= (2^{2} * 2^{0.5}) - (2^{1} * 2^{0.5)}\]
factor out the 2^0.5
\[= 2^{0.5}(2^{2} - 2^{1)}\]
\[=2^{0.5} * 2^{1}\]
\[=2^{1.5} = 2^{3/2}\]