Simplify
(p^-4+m p^2m)^-4/
(p^-4)-m
To simplify the expression, we can start by expanding the numerator and denominator of the fraction separately.
Let's begin with the numerator:
(p^-4+m p^2m)^-4
First, we can bring the exponent -4 on the outside by applying the negative exponent rule:
p^4 * (m p^2m)^4
Now let's expand the expression within the parentheses, (m p^2m)^4:
(m^4) * (p^2m)^4
Next, simplify the exponent of m^4:
(m^4) * (p^8m^4)
Now, let's simplify the denominator:
(p^-4)-m
Using the negative exponent rule, we can rewrite p^-4 as 1/p^4:
(1/p^4) - m
Now we can combine the numerator and denominator:
[(m^4) * (p^8m^4)] / [(1/p^4) - m]
To simplify further, let's take care of the term in the denominator by multiplying it by the common denominator, which is p^4:
[(m^4) * (p^8m^4)] / [(1/p^4)*p^4 - m*p^4]
Simplifying the denominator further:
[(m^4) * (p^8m^4)] / [1 - mp^4]
Finally, we have simplified the expression to:
(m^4 * p^8m^4) / (1 - mp^4)