How do you write #((5^(2/3))^(1/5))^2# in radical form?

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Answer 1 · 2018-01-29T00:12:32

See a solution process below:

First, use this rule of exponents three times to simplify the expression:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#((5^(2/3))^color(red)(1/5))^color(blue)(2) => (5^(2/3))^(color(red)(1/5) xx color(blue)(2)) => (5^(2/3))^color(blue)(2/5)#

#(5^color(red)(2/3))^color(blue)(2/5) => 5^(color(red)(2/3) xx color(blue)(2/5)) => 5^(4/15)#

Next, use the same rule in reverse to rewrite the expression as:

#5^(4/15) => 5^(color(red)(4) xx color(blue)(1/15)) => (5^color(red)(4))^color(blue)(1/15) => 625^(1/15)#

Now, use this rule of radicals and exponents to rewrite the expression in radical form:

#x^(1/color(red)(n)) = root(color(red)(n))(x)#

#625^(1/color(red)(15)) = root(color(red)(15))(625)#