Question

Find the value of m​

Answer 1

m = 9

Explanation:

Using the rules of exponents

`(a^m)^(n)` =
`a^(mn)`

`a^(m)` ×
`a^(n)` ⇔
`a^((m+n))`

`a^(-m)` =
`(1)/(a^(m) )`

Then

`((1)/(27)) ^(m)` ×
`(81)^(-1)` = 243 ← express all values to base 3

`((1)/(3^3)) ^(m)` ×
`(3 ^4)^(-1)` =
`3^(5)`

`(3^-3)^(m)` ×
`3^(-4)` =
`3^(5)`

`3^(-3m)` ×
`3^(-4)` =
`3^(5)`

`3^((-3m-4))` =
`3^(5)`

Since bases on both sides are equal, both 3 , then equate exponents

- 3m - 4 = 5 ( add 4 to both sides )

- 3m = 9 ( divide both sides by - 3 )

m = - 3