How do you write #sqrt(2^(5/8))# as a radical?

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Answer 1 · 2018-06-03T19:59:20

See a solution process below:

We can rewrite the expression as:

#(2^(5/8))^(1/2)#

Next, we can use this rule of exponents to eliminate the outer exponent:

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

#(2^color(red)(5/8))^color(blue)(1/2) => 2^(color(red)(5/8) xx color(blue)(1/2)) => 2^(5/16)#

Then, we can use the reverse of the rule above to rewrite the expression as:

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

#2^(color(red)(5) xx color(blue)(1/16)) => (2^color(red)(5))^color(blue)(1/16) => 32^16 => root(16)(32)#