Applied Calculus
posted by Jacob on .
2^(3/4)*4^(3/2)

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!

since 4=2^2,
4^(3/2) = (2^2)^(3/2) = 2^3
2^(3/4) * 2^3 = 2^(3/43) = 2^(9/4)
= 1/(4*2^(1/4)) = 0.21
Or, if you want positive exponents from the getgo,
4^(3/2) = 1/4^(3/2)
2^(3/4) / 4^(3/2)
= 2^(3/4) / 2^3
= 1 / 2^(9/4)
= 0.21