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

Answer:

$k=3+6x$.

Step-by-step explanation:

We haven been given an expression $27\times 9^{3x}$. 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:

$3^3\times (3^2)^{3x}$

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

$3^3\times 3^{2\cdot 3x}$

$3^3\times 3^{6x}$

Using exponent property $a^b\times a^c=a^{b+c}$, 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 $3+6x$.

Answer 2

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