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Answer 1 · 2016-01-07T15:35:15

#25^(3/4)=5*root(4)(5^2)#

The properties of Exponents tell us that:

#a^(n/m)=root(m)(a^n)#

and

#(a^p)^q=a^(p*q)#

and

#a^h*a^k=a^(h+k)#

then:

#25^(3/4)=root(4)(25^3)=root(4)((5^2)^3)=root(4)(5^6)=#
#=root(4)(5^4*5^2)=root(4)(5^4)*root(4)(5^2)=5root(4)(5^2)#