How do you simplify #7^(2/3)#?

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Answer 1 · 2018-03-27T12:22:50

See a solution process below:

First, we can rewrite the expression as:

#7^(color(red)(2) xx color(blue)(1/3))#

Next, we can use this rule of exponents to simplify the expression:

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

#7^(color(red)(2) xx color(blue)(1/3)) => (7^(color(red)(2)))^color(blue)(1/3) => 49^(1/3)#

If necessary we can use this rule for exponents and radicals to write this expression in radical form:

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

#49^(1/color(red)(3)) = root(color(red)(3))(49)#