How do you write the expression #(sqrt10)^3# in exponential form?

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Answer 1 · 2018-06-07T15:22:02

#10^(3/2)#

Definition for rational exponents:

#rootcolor(red)n(a^color(blue)m) = a^(color(blue)m/color(red)n)#

#(sqrt(10))^3#

#(10^(1/2))^3#

now use rule:

#(a^n)^m = a^(m*n)#

#(10^(1/2))^3 = 10^(3/2)#