Question

Plz help. Attachment below

Answer 1

The value of k is 1.

Explanation:

You have to apply Indices Law :

`{a}^(m) * {a}^(n) = {a}^(m + n)`

For this question :

`{( (4)/(5) )}^(2) * {( (4)/(5) )}^(5) = {( (4)/(5) )}^(6k + 1)`

`{( (4)/(5)) }^(2 + 5) = {( (4)/(5)) }^(6k + 1)`

`by \: comparison`

`2 + 5 = 6k + 1`

`7 = 6k + 1`

`7 - 1 = 6k`

`6k = 6`

`k = 6 / 6`

`k = 1`

Answer 2

k = 1

Explanation:

`a^(m) * a^(n) = a^(m+n)\\\\((4)/(5))^(2)*((4)/(5))^(5)=((4)/(5))^(6k+1)\\\\\\((4)/(5))^(2+5)=((4)/(5))^(6k+1)\\\\((4)/(5))^(7)=((4)/(5))^(6k+1)`

Compare the powers,

6k + 1 = 7 {subtract 1 from both sides}

6k = 7 - 1

6k = 6 {Divide both sides by 6}

6k/6= 6/6

k = 1