Question

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

Find p in the equation ( attached photo of the equation)

Answer 1

p = - 14

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