Question

27 x 9 ^3x can be written in the form 3^k Find out what k is an expression in term of x

Answer 1

k = 3 + 6x

note that 27 = 3³ and 9 = 3²

27 ×
`9^(3x)` = 3³ × (3²)^3x = 3³ ×
`3^(6x)` =
`3^(3 + 6x)`

hence k = 3 + 6x

Answer 2

`k=3+6x`.

Step-by-step explanation:

We haven been given an expression
`27* 9^(3x)`. We are asked to write our given expression is form
`3^k` and find out value of k.

We can rewrite 27 as
`3^3` and 9 as
`3^2`. Upon substituting these values in our given expression, we will get:

`3^3* (3^2)^(3x)`

Using exponent property
`(a^b)^c=a^(b\cdot c)`, we will get:

`3^3* 3^(2\cdot 3x)`

`3^3* 3^(6x)`

Using exponent property
`a^b* a^c=a^(b+c)`, we will get:

`3^(3+6x)`

We have written our given expression in form
`3^k`:

`3^(k)=3^(3+6x)`

Therefore, the value of k is
`3+6x`.