First, we can use these rules for exponents to simplify the term on the left of the expression:
#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#(3^color(red)(1)p^color(red)(1))^color(blue)(4)(3p^-9) = (3^(color(red)(1)xxcolor(blue)(4))p^(color(red)(1)xxcolor(blue)(4)))(3p^-9) = (3^4p^4)(3p^-9) =#
#(81p^4)(3p^-9)#
We can next rewrite this expression as:
#(81 xx 3)(p^4p^-9) = 243p^4p^-9#
Then, we can use this rule for exponents to simplify the #p# terms:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#243p^color(red)(4)p^color(blue)(-9) = 243p^(color(red)(4) + color(blue)(-9)) = 243p^-5#
If we want an expression with no negative exponents we can now use this rule for exponents:
#x^color(red)(a) = 1/x^color(red)(-a)#
#243p^color(red)(-5) = 243/p^color(red)(- -5) = 243/p^5#
The solution to this problem is:
#243p^-5# or #243/p^5#
