Question

2^(3/4)*4^(-3/2)

Answer 1

I know how to solve it to get .21, but I need to write it using positive exponents only. I know this isn't technically Calculus, but it is what we are reviewing currently. I am a bit rusty with this one, can't quite remember how to do it. I am trying some different things, but would greatly appreciate an explanation. Thank you!

Answer 2

since 4=2^2,
4^(-3/2) = (2^2)^(-3/2) = 2^-3

2^(3/4) * 2^-3 = 2^(3/4-3) = 2^(-9/4)
= 1/(4*2^(1/4)) = 0.21

Or, if you want positive exponents from the get-go,

4^(-3/2) = 1/4^(3/2)

2^(3/4) / 4^(3/2)
= 2^(3/4) / 2^3
= 1 / 2^(9/4)
= 0.21