How do you simplify #243^{\frac{5}{2}}#?

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Answer 1 · 2016-10-21T23:49:56

#920,482.81#

Using Logarithmic approach:
#243^(5/2)#
#243^2.5#

#Log 243 = 2.3856063#

#2.5 * Log 243 = 2.5 * 2.3856063 = 5.9640157#

antilog #5.9640157 = 920,482.81#

Answer 2 · 2016-10-22T12:22:14

If the question was meant to be be #243^(2/5)#

Answer is #9#

I suspect that there is a problem with the question itself and a typo has crept in.

#243 = 3^5#.

#243# therefore has an exact 5th root, but not an exact square root which is being asked.

Consider if the question was meant to be be #243^(2/5)#

This now means: #(color(red)(root5 243))^2#

= #color(red)(3)^2#

=#9#