Respuesta :
We have been given an expression [tex]\left(\dfrac {6}{17}\right)^{9x}[/tex]. We are asked to find the value of A when rewrite our given expression as [tex]A^{x}[/tex].
To solve our given problem, we will use exponent properties.
Using exponent property [tex]a^{mn}=(a^m)^n[/tex], we can rewrite our given expression as:
[tex]\left(\dfrac {6}{17}\right)^{9x}=\left(\left(\dfrac {6}{17}\right)^9\right)^{x}[/tex]
Now, we will compare our expression with [tex]A^{x}[/tex].
Upon comparing [tex]\left(\left(\dfrac {6}{17}\right)^9\right)^{x}[/tex] with [tex]A^{x}[/tex], we can see that [tex]A=\left(\dfrac {6}{17}\right)^9[/tex].
Therefore, the value of A is [tex]\left(\dfrac {6}{17}\right)^9[/tex].
We can further simplify [tex]\left(\dfrac {6}{17}\right)^9[/tex] as:
[tex]\left(\dfrac {6}{17}\right)^9=\frac {6^9}{17^9}=\frac{10077696}{118587876497}[/tex]
The value of A is [tex]\left( \dfrac{6}{17}\right)^{9}[/tex].
Given that,
Equation; [tex]\rm \left(\dfrac{6}{17}\right)}^{9x}[/tex]
We have to find,
The value of A when the function is written as [tex]\rm A^x[/tex]?
According to the question,
To determine the value [tex]A^x[/tex] by applying the exponent property in the equation following all the steps given below.
By using the exponent property rewrite the equation,
[tex]\rm \left ( a )\right ^{mn} = ( a^m )\right^{n}[/tex]
Applying the property in the equation,
[tex]\rm \left(\dfrac{6}{17}\right)}^{9x}= \left( \left(\dfrac{6}{17}\right)^{9}\right) \right)^{x}[/tex]
By comparing the equation with [tex](A)^{x}[/tex],
[tex]\rm A ^{x}= \left( \left(\dfrac{6}{17}\right)^{9}\right) \right)^{x}\\\\A = \left( \dfrac{6}{17}\right)^{9}[/tex]
Hence, The required value of A is [tex]\left( \dfrac{6}{17}\right)^{9}[/tex].
For more details click the link given below.
https://brainly.com/question/1807508
