https://file.aiquickdraw.com/mathbot/file/1728065240433x0j6jivp.jpg

The equation shown in the image is:

\[
\left( \frac{2}{3} \right)^x = \frac{1}{16}
\]

### Solution:

We need to solve for \( x \).

1. First, express \( \frac{1}{16} \) as a power of 2:
   \[
   \frac{1}{16} = 2^{-4}
   \]

2. Now, we rewrite the equation:
   \[
   \left( \frac{2}{3} \right)^x = 2^{-4}
   \]

3. To solve this, take the logarithm of both sides, but first let's note that the right side is not yet comparable in the base sense to the left side. One approach involves understanding that on the left side, both 2 and 3 are not simple powers of each other.

One practical option is solving this logarithmically, which might require some extra steps; however, one direct observation is

Solve the exponential equation (2/3)^x = 1/16 by expressing 1/16 as a power of 2 and using logarithmic methods. Understand key algebraic concepts including logarithmic properties and the laws of exponents. Suitable for high school students in Grades 9-11.

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