Answer:
p = - 14
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex]
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]
Note 81 = 9² and 729 = 9³
Given
[tex](81)^{-4}[/tex] ÷ [tex](729)^{2-p}[/tex]
= [tex](9^{2}) ^{-4}[/tex] ÷ [tex](9^{3}) ^{2-p}[/tex]
= [tex]9^{-8}[/tex] ÷ [tex]9^{6-3p}[/tex]
= [tex]9^{-8-(6-3p)}[/tex]
= [tex]9^{-8-6+3p}[/tex]
= [tex]9^{3p-14}[/tex]
Thus
[tex]9^{3p-14}[/tex] = [tex]9^{4p}[/tex]
Since bases on both sides are equal then equate the exponents
4p = 3p - 14 ( subtract 3p from both sides )
p = - 14
