https://file.aiquickdraw.com/mathbot/file/172650691715990prx1qt.jpg

The given equation in the image is:

\[
\frac{8}{27} = 2^n
\]

We need to solve for \( n \).

### Step-by-step solution:

1. Express \( 8 \) and \( 27 \) as powers of base numbers:
   \[
   8 = 2^3 \quad \text{and} \quad 27 = 3^3
   \]

   So, we can rewrite the fraction:
   \[
   \frac{8}{27} = \frac{2^3}{3^3} = \left(\frac{2}{3}\right)^3
   \]

2. Now the equation becomes:
   \[
   \left(\frac{2}{3}\right)^3 = 2^n
   \]

3. To make the powers of \( 2 \) on both sides comparable, we equate the exponents. Notice that the left-hand side also contains \( 3 \), so it doesn't match perfectly with \( 2^n \).

Thus, there is no integer value of \( n \) that makes this equation true. The equation as presented seems tricky because it mixes a fraction and a pure power of 2.

Would you like a different approach or further clarification on this equation? 

### Related Questions:
1. How do you solve fractional exponent equations?
2. How do you express numbers as powers of prime factors?
3. What is the method to solve equations involving different bases like powers of 2 and 3?
4. Can logarithms be used to solve equations like this?
5. How do you interpret non-integer powers in equations?

**Tip**: Always check if both sides of an equation can be expressed using the same base for easier comparison.

This problem involves solving for the variable n in the equation 8/27 = 2^n by expressing both sides as powers of base numbers. Learn how to apply exponent rules to solve equations involving fractional powers. Suitable for students in Grades 9-12.

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