How do you simplify # 9^(5/2)#?

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Answer 1 · 2018-04-02T18:50:09

The simplified expression is #243#.

You can rewrite the fractional exponent as roots and powers, like this:

#color(white)=x^(color(red)m/color(blue)n)=root(color(blue)n)(x^color(Red)m) or (root(color(blue)n)(x))^color(Red)m#

We can use this in our expression:

#color(white)=9^(color(red)5/color(blue)2)#

#=(rootcolor(blue)2 9)^color(red)5#

#=(sqrt9)^color(red)5#

#=(3)^color(red)5#

#=3^color(red)5#

#=243#

That's it. You can check the answer using a calculator: