First, we can use this rule of exponents to rewrite this expression:
#x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)#
#(5x)^(2/5) = (5x)^(color(red)(2) xx color(blue)(1/5)) = ((5x)^color(red)(2))^color(blue)(1/5)#
We can now use these rules for exponents to rewrite the term within the parenthesis:
#a = a^color(red)(1)# and the reverse of the rule we used above: #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#((5x)^2)^(1/5) = ((5^color(red)(1)x^color(red)(1))^color(blue)(2))^(1/5) = (5^(color(red)(1) xx color(blue)(2))x^(color(red)(1) xx color(blue)(2)))^(1/5) = (5^2x^2)^(1/5) = (25x^2)^(1/5)#
We can now use this rule of exponents and radicals to write the expression in radical form:
#x^(1/color(red)(n)) = root(color(red)(n))(x)#
#(25x^2)^(1/color(red)(5)) = root(color(red)(5))(25x^2)#
