Question

Simplify 9^(2/3)#?

Answer 1

See the entire solution process below:

Explanation:

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)`