How do you simplify #\frac { ( 4^ { 8} ) ^ { 2} } { 16}#?

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Answer 1 · 2018-04-05T17:36:07

See a solution process below:

First, use this rule of exponents to rewrite the numerator:

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

#(4^color(red)(8))^color(blue)(2)/16 =>#

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

#4^16/16#

Next, rewrite the denominator as:

#4^16/4^2#

Now, use this rule of exponents to simplify the expression as:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#4^color(red)(16)/4^color(blue)(2) =>#

#4^(color(red)(16)-color(blue)(2)) =>#

#4^14#

Or

#268,435,456#