Question

Please help!! Please give step by step so i can understand

Answer 1

Answer:

p = - 14

Step-by-step explanation:

Using the rules of exponents

$a^{m}$ ÷ $a^{n}$ = $a^{(m-n)}$

$(a^{m}) ^{n}$ = $a^{mn}$

Note 81 = 9² and 729 = 9³

Given

$(81)^{-4}$ ÷ $(729)^{2-p}$

= $(9^{2}) ^{-4}$ ÷ $(9^{3}) ^{2-p}$

= $9^{-8}$ ÷ $9^{6-3p}$

= $9^{-8-(6-3p)}$

= $9^{-8-6+3p}$

= $9^{3p-14}$

Thus

$9^{3p-14}$ = $9^{4p}$

Since bases on both sides are equal then equate the exponents

4p = 3p - 14 ( subtract 3p from both sides )

p = - 14