First, use this rule of exponents to simplify the denominator of the fraction:
a^color(red)(0) = 1a0=1
(-m^-2n^-4)/((2m^-2n^4p^-3)^color(red)(0) * 2m^2n^-4p^-1) =>−m−2n−4(2m−2n4p−3)0⋅2m2n−4p−1⇒
(-m^-2n^-4)/(1 * 2m^2n^-4p^-1) =>−m−2n−41⋅2m2n−4p−1⇒
(-m^-2n^-4)/(2m^2n^-4p^-1)−m−2n−42m2n−4p−1
Next, rewrite the expression as:
(-1m^-2n^-4)/(2m^2n^-4p^-1) =>−1m−2n−42m2n−4p−1⇒
-1/2(m^-2/m^2)(n^-4/n^-4)(1/p^-1) =>−12(m−2m2)(n−4n−4)(1p−1)⇒
-1/2(m^-2/m^2)(color(red)(cancel(color(black)(n^-4)))/color(red)(cancel(color(black)(n^-4))))(1/p^-1) =>
-1/2(m^-2/m^2) * 1 * (1/p^-1) =>
-1/2(m^-2/m^2)(1/p^-1)
Next, use this rule for exponents to simplify the m terms:
x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))
-1/2(m^color(red)(-2)/m^color(blue)(2))(1/p^-1) =>
-1/2(1/m^(color(blue)(2)-color(red)(-2)))(1/p^-1) =>
-1/2(1/m^(color(blue)(2)+color(red)(2)))(1/p^-1) =>
-1/2(1/m^4)(1/p^-1) =>
-1/(2m^4)(1/p^-1)
Now, use these rules for exponents to simplify the p term:
1/x^color(red)(a) = x^color(red)(-a) and a^color(red)(1) = a
-1/(2m^4)(1/p^color(red)(-1)) =>
-1/(2m^4)(p^color(red)(- -1)) =>
-1/(2m^4)(p^color(red)(1)) =>
-1/(2m^4)(p) =>
-p/(2m^4)
