https://file.aiquickdraw.com/mathbot/file/1725417555553qiicvdow.jpg

To solve the equation given in the image:

\[
\frac{1}{3^4} = z^y
\]

First, let's simplify the left-hand side:

\[
\frac{1}{3^4} = 3^{-4}
\]

So, the equation becomes:

\[
3^{-4} = z^y
\]

For this equation to hold, the value of \( z \) must be 3 (or a related base) and \( y \) must be such that \( z^y = 3^{-4} \). The simplest way to satisfy this equation is by setting \( z = 3 \) and \( y = -4 \). This is because:

\[
3^{-4} = 3^y
\]

Thus, \( y = -4 \).

The solution is:
- \( z = 3 \)
- \( y = -4 \)

Would you like further details or explanations? Here are 5 related questions for practice:

1. If \( 4^x = 16 \), what is the value of \( x \)?
2. Solve for \( x \): \( 2^x = 8 \).
3. If \( y = 2x \) and \( 3^y = 27 \), find \( x \).
4. What is the value of \( z \) if \( z^3 = 64 \)?
5. Solve for \( a \): \( 5^a = 1/25 \).

**Tip:** When dealing with exponential equations, always consider rewriting both sides of the equation using the same base for easier comparison and solution.

Find the values of z and y that satisfy the equation: 1/3^4 = z^y

This page explains how to solve the exponential equation 1/3^4 = z^y. The solution covers the core concept of exponentiation and how to manipulate exponents, making it suitable for students in Grades 8-10.

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