Simplify 9^(2/3)#?

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Answer 1 · 2017-04-10T21:55:46

See the entire solution process below:

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)#

#9^(2/3) = 9^(color(red)(2) xx color(blue)(1/3)) = (9^color(red)(2))^color(blue)(1/3)#

#9^2 = 81# so we can rewrite this as:

#(9^color(red)(2))^color(blue)(1/3) = 81^(1/3)#

Next, we can use the rule of radicals and exponents to continue the simplification:

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

#81^(1/color(red)(3)) = root(color(red)(3))(81)#

Now, we can rewrite the term within the radical and complete the simplification as:

#root(3)(81) = root(3)(27 * 3) = root(3)(27)root(3)(3) = 3root(3)(3)#