First, use this rule of exponents to eliminate the negative exponent in the numberator:
#x^color(red)(a) = 1/x^color(red)(-a)#
#2^color(red)(-1)/(2^3 * (2^2)^-4) => 1/(2^color(red)(- -1) * 2^3 * (2^2)^-4) => 1/(2^color(red)(1) * 2^3 * (2^2)^-4)#
We can next use this rule of exponents to get simplify the term with the outer exponent:
#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#1/(2^1 * 2^3 * (2^color(red)(2))^color(blue)(-4)) => 1/(2^1 * 2^3 * 2^(color(red)(2) xx color(blue)(-4))) => 1/(2^1 * 2^3 * 2^-8)#
Then, we can use this rule of exponents to combine the terms in the denominator:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#1/(2^color(red)(1) * 2^color(blue)(3) * 2^color(green)(-8)) => 1/(2^(color(red)(1) + color(blue)(3) + color(green)(-8))) = 1/2^-4#
Now, use this rule of exponents to complete the simplification:
#1/x^color(red)(a) = x^color(red)(-a)#
#1/2^color(red)(-4) => 2^color(red)(- -4) => 2^color(red)(4) => 16#