How do you evaluate and simplify $16^(3/2)$ ?

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Answer 1 · 2017-02-03T16:51:34

See the entire solution process below:

First, we can use this rule of exponents to rewrite this expression:

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

$16^(3/2) = 16^(color(red)(1/2) xx color(blue)(3)) = (16^color(red)(1/2))^color(blue)(3)$

We can rewrite and simplify this as:

$(16^color(red)(1/2))^color(blue)(3) = (sqrt(16))^color(blue)(3) = 4^color(blue)(3)$

Now, we can simplify this to:
$4^color(blue)(3) = 4 xx 4 xx 4 = 16 xx 4 = 64$

How do you evaluate and simplify 16^(3/2)16^(3/2)?