Question

What is the value of AAA when we rewrite \left(\dfrac {6}{17}\right)^{9x}( 17 6 ​ ) 9x (, start fraction, 6, divided by, 17, end fraction, ), start superscript, 9, x, end superscript as A^{x}A x A, start superscript, x, end superscript ?

Answer 1

We have been given an expression $\left(\dfrac {6}{17}\right)^{9x}$. We are asked to find the value of A when rewrite our given expression as $A^{x}$.

To solve our given problem, we will use exponent properties.

Using exponent property $a^{mn}=(a^m)^n$, we can rewrite our given expression as:

$\left(\dfrac {6}{17}\right)^{9x}=\left(\left(\dfrac {6}{17}\right)^9\right)^{x}$

Now, we will compare our expression with  $A^{x}$.

Upon comparing $\left(\left(\dfrac {6}{17}\right)^9\right)^{x}$ with $A^{x}$, we can see that $A=\left(\dfrac {6}{17}\right)^9$.

Therefore, the value of A is $\left(\dfrac {6}{17}\right)^9$.

We can further simplify $\left(\dfrac {6}{17}\right)^9$ as:

$\left(\dfrac {6}{17}\right)^9=\frac {6^9}{17^9}=\frac{10077696}{118587876497}$